The ship lineages and technological progression really depends a lot on the narrative timeline. I think the culture of Star trek fandom of the later 90's and early 2000s presented a timeline somewhat like we saw in Enterprise. What Enterprise added was that human were held back. But other than that, the common idea was that humans joined an already existing interstellar community. I'm not sure if this idea originated with FASA or Trek novels, or what not. However, excluding Enterprise, and looking at exclusively what's seen on screen my Trek history timeline became very different.
What important to note is that there are no conclusive references stating that Vulcanians or any other local species had FTL travel. Related to that is the fact that Zefram Cochrane is the one recognized as inventing warp drive, even by Spock. If he was just one of many, then he probably wouldn't have been so celebrated. Another important point is the prominence of humanity in the Star Trek universe. I think this strongly implies that we got a big foothold first. With these considerations in mind, my rough ship evolution timeline is as follows:
- 21st Century -
1990s-2018 - Inner system exploration with DY-100s and other craft. We might have reached Jupiter at this point.
2018-2030s - Sleeper ships are replaced by faster propulsion, possibly nuclear rocket engines. There is a mix of big ships like the DYs and smaller exploration ships like the Ares 4. Colonization also expands to include outer solar system.
2030s-2062 - The solar system has a great deal of colonization at this point. Uranus and Neptune have been explored to some extent. Now humanity is pushing out of the solar system. Advances in fusion drives enable a colonization mission to Alpha Centauri. During this time Zefram Cochrane and various government agencies begin to researching space warp technology. World War III breaks out and earth's contribution to the solar community is severely curtailed. However, the Solar system still has a large economic reliance upon earth. WWIII comes to a close with the nuking of major cities in the 2050s, and the ensuing economic and political collapse renders earth a bit player in space affairs. This is a huge hit to colonies in the solar system, who now scramble to become more self reliant; and now resent earth for blowing themselves up. Zefram Cochrane, seeing the profit potential for a warp drive, continues his research as much as possible during the war and after ward.
2063 - The first manned warp ship is launched and successfully tested. By sheer coincidence a sublight Vulcanian research ship is passing through the Solar system on a survey mission. They detect the signs of the Phoenix's warp drive which for them was only theoretical. The Vulcanians recognized the importance of this discovery and decide to interrupt their mission and land on earth.
Late 2060s - The Vulcanians landing on earth doesn't have a huge impact, because they aren't that much more advanced than us, and people are doubtful that they're extraterrestrials. After some work, Zefram Cochrane begins gathering allies to further develop the space warp. Eventually test flights are conducted to Alpha Centauri. Zefram Cochrane moves to Alpha Centauri and sets up his primary research facility there. Basically the idea is that ships zip back and forth between earth and Alpha Centauri to test out their propulsion systems. However, the trip still takes a few months, and any communication must be done by messages downloaded into the ships computer. Otherwise it would still take radio four years to span the distance.
Also during this period, after some successful tests, an old cargo ship the S.S. Valiant is retro fitted with warp drive. It's first mission is to return some of the Vulcanian crew to their home planet. After that it continues on its mission to explore other planets. The S.S. Valiant is eventually lost.
Humanity is excited about the potentials of the space warp drive. This invention gradually redeems earth in the eyes of many solar system inhabitants and humanity begins to come together. FTL probes are sent out soliciting the friendship of any intelligent species as well as offering them information on how to construct FTL technology.
Late 21st Century - Unfortunately, not all species are friendly. The Kzinti receive the information from one of these probes and develop FTL ships. They also decide humans look particularly tasty. This leads to the Kzin wars. (Yes, I disregard TAS's dating.) Ships of this time start out mainly as existing ships modified with FTL drives. Though, in the 2070s we get out first purpose built warp drive ship the S.S. Bonaventure. The design of the Bonaventure is considered to be the result of the eccentricity of it's creator and is deemed impractical. Other ships of the time are pretty basic in design. Imagine a better designed S.S. Valiant, or something like the Starship Velocity from Pacific 201.
- 22nd Century -
Early 22nd century - There still isn't a lot of anti-matter in existence and so most ships have some form of multistage or anti-matter spiked fusion drives. Because of their superior capabilities in warping space-time, warp nacelle begin transitioning to ring shaped designs. Ships take on some of the characteristics that we later see in the XCV-330, but there is still a lot of variety in design, such as the DY lineage.
Also during this time humanity is dominating space affairs with many colonies and cultural influences on many worlds. Even the planet Vulcan and its people get their name from human visitors calling the place "hot as Vulcan". They are essentially culturally conquered by humanity's representation of them. And while not being done maliciously, other inhabited worlds such as those of the Andorians, Tellarites, etc. are sometimes reduced to caricatures of their pre-contact cultures (somewhat analogous to Native Americans, Hawaii, or Chinese food).
The Earth Federation is founded to help manage the many earth colonies and allied alien worlds. The United Earth Space Probe Agency is the primary exploration and military arm of the Earth Federation.
2150s-2160s - The S.S. Enterprise UEV-47 ringship is launched. It is a mid range exploration vessel capable of missions up to two years. It's not the best of the best as there other ships that have greater capabilities.
During this time earth makes contact with a strange alien species. They are from a star system known to earth as Romulus, named after twin exoplanets that were discovered orbiting it. These twin planets were named Romulus and Remus after twin brothers in the founding narrative of Rome. Contact with these aliens doesn't go well and war breaks out. Due to the method of combat and nuclear weapons, no visual contact is ever actually made with the Romulans.
However, due to this conflict, many alien allies exemplified how invaluable they were to the Earth Federation and are able to push for greater influence in the interstellar stage. As a result the Earth Federation is reorganized and the United Federation of Planets is founded. A new scientific/military branch is founded called Starfleet. However, even with this new Federation, humans still dominated. The UFP would still occasionally be referred to as the "Earth Federation" and Starfleet would still largely rely on UESPA for another 100 years. The S.S. Enterprise is given to the newly founded UFP and is renamed as the U.S.S. Enterprise XCV-330.
Besides the war revolutionary discoveries are made in this time, many almost on par with the discovery of the space warp. First, is the discovery of subspace. By the end of the war this parallel sub-spacial dimension is able to be utilized for FTL communication. This invention brings about the end of the "pony express" era of FTL data transmission; which was done by having data stored and carried on board ships. Planets and colonies are now able to be directly linked through subspace communication.
Second, is the discovery of gravity manipulation technology. On one of the missions of the S.S. Enterprise, its crew discovered a stasis box left behind by a long lost civilization known as "the Slavers". Inside this stasis box was a belt that was capable of manipulating gravity fields. Earth scientists were able to reverse engineer this flying belt to some extent. The resulting research enabled the creating artificial gravity fields for use on space craft. 1G acceleration burns and adhesive footwear are largely rendered obsolete by this technology.
Late 22nd Century - Advances in meta-materials, and antimatter production, improve the capability of linear warp nacelles. These types of nacelles begin to rise in prominence over the ring shaped engines. The combination of this and artificial gravity technology results in the most advanced ship to date, the Daedalus class. Starships of this era are able to perform amazing feats such as subspace radio communication over long distances, unconventional orbital patterns, and unprecedented travel times.
- 23rd Century -
Early 23nd Century - Ship designs of this era result in ships taking on a more saucer-like appearance to take advantage of the floor space enabled by the artificial gravity technology. However, travel times eventually reach a limit. Due to the unique nature of warping space time an upper limit is reached. Extremely fast speeds are found to cause time distortion between the spacecraft and the outside universe. These distortions essentially create a practical upper limit called the Time Barrier.
However, there are two notable discoveries during this era first is the transporter, which was discovered by reverse engineering a derelict alien spacecraft. This technology enables the teleportation of objects across certain distances to designated target coordinates. Early versions of this technology are slow, taking minutes to teleport the subject.
Invented in the early to mid 23nd century, the other discovery is that of improved space warp travel. This technology, is dubbed "time warp", and allows the breaking of the Time Barrier. Even greater speeds are now possible.
2240s-2260s - The result of all this technology is put together in one package, the Constitution Class, a sub-type of the Starship Class. This ship is the ultimate Swiss army knife of a ship, from exploration, to patrolling, to cargo transportation. This ship can do it all.
Yet, even with the great advancements, this time is not without conflict. Increasing tensions between member worlds in the, still largely human, United Federation of Planets result in a short lived conflict, known by some as the "Federation Civil War." This war concluded with the victory of Fleet Captain Garth at the battle of Axanar. In later years peace missions at Axanar would heal the wounds of this conflict and provide greater unity and brotherhood among the worlds of the Federation. Non-human member worlds are able to reach an unprecedented level of sovereignty and equality within the Federation.
In the Late 2260s UESPA is largely phased out and Starfleet has taken over most of its former operations.
2270s - After twenty years of operations the Constitution class is getting dated and at various times the remaining ships are called in for major refits.
The next greatest ship in Stafleet's line up is the Miranda class. It has a larger internal volume than the refitted Constitution while fitting into a more compact package. Variants of this type of starship will continue to serve Starfleet for more than 100 years.
2280s - This decade saw a huge advancement in warp drive technology. Discoveries were made that enabled subspace to be used for FTL travel. It had heretofore been only used for communication. the technology proved that a space craft could be pushed into subspace, thus enabling it to travel faster than had previously been able to in normal space. After several successful prototype runs, this new type of warp, called "transwarp", is built into the U.S.S. Excelsior NX-2000. Despite a few minor initial setbacks, the transwarp drive of the U.S.S Excelsior is a complete success. This transwarp drive is implemented into all starship designs from this time forward.
Late 23rd Century - The Excelsior style ships become a workhorse for the Federation and will continue to be used for 100 years.
- 24th Century -
Early 24th Century - This era saw improvements and refinements in previous starship technologies.
Mid 23rd Century - A lengthy era of peace results in the Galaxy and Nebula Class designs which are exploration ships, but also capable of hosting the families of the crew. Prior to this families had been rare. These large luxurious ships are revolutionary in their function as well as their technological innovations such as the holodeck. The holodeck enables extremely realistic training and simulation opportunities.
Late 23rd Century - The Dominion War pushes the Federation to the brink and causes Starfleet to completely revise its design philosophy. Starships became much more spartan and combat focused. We see innovative designs such as the Defiant; the intrepid class; and even the Prometheus class with its multi-vector assault mode.
The U.S.S. Voyager, which had been lost in the Delta Quadrant, returns and brings with it a host of revolutionary technology. Much of this technology is still being researched.
Conclusion
Oh, boy, that turned out longer than I expected. I apologize for the lengthy read. I did miss a few things like the invention of phasers and the disastrous first contact with the Klingons. Also at some point between 2150 and 2260 the energetic properties of dilithium are discovered and integrated into ships power systems. However, most of the information is there. I think this timeline explains a lot more of what we see on screen rather than the common fan narrative and the history presented by Enterprise.