I suppose there are two ways of looking at this... one being STAR TREK in-universe, the other derived from the TREK universe (a parallel universe?) using TREK as a kind of template or guide...
STAR TREK (in-universe)
Pardon my delving into canon, but ENT did provide some useful clues:
Capt. Archer was central to a diplomatic initiative that resulted in the temporary formation of a
Coalition of Planets prior to the escalation in hostilities that became the Earth-Romulan Conflict; this would've been in the later half of the 2150s. (2154 + 4th season = 2158?) Earth Starfleet seemed to be part of the core group that coordinated this coalition at that time. The discussion started in ENT's "
United" and continued through
"Terra Prime". It was even mentioned roundly in "
These Are the Voyages..." that Archer's spearheading of the Earth initiative to continue the Coalition would quickly morph into the Federation. So it would seem all the pieces are already there.
So obviously Earth Starfleet was no only instrumental in the ass-backwards reorganization of the Coalition of Planets into the Federation, but also in founding the Federation Starfleet as well. In "These Are the Voyages", Tripp and Archer toast to Warp 7, a hint at the first-generation of Federation starships with a new generation of warp propulsion. I see the early Federation Starfleet coalescing around a few key concepts: (1: basic diplomatic and administrative organization; probably derived from the Coalition's wartime effort; (2: drafting a basic statement of mission from which all fleet tasks and regulations would be derived, like a Constitution of sorts that would guide civilian control of Starfleet Command; (3: those interested Coalition/Federation partners would draft a technological template for new Warp 7 starships, Federation starbases, shipping services, telecommunications, etc.; and (4: finding a way for different species to work together, both in terms of facilities and protocols. (so that Tellarites and Andorians don't start picking fights, but instead find a way to work together)
TREK-derived parallel Universe
This one is tricky. If the Vulcans aren't there guiding (and politicizing) United Earth Space Probe Agency's program, then it is harder to imagine a Coalition forming. It seemed to me that at least someone in the Vulcan High Command was working with the Romulans to disrupt Earth and stop the Coalition from forming (or to defeat it). Take Vulcan out of that equation and you're looking at a different situation entirely.
If Earth and other advanced nearby worlds were compelled to form an alliance because of a mysterious Romulan (or other alien) security threat, then someone would have to be at the core of it. If the participating worlds formed a combined Coalition fleet that would become the Federation, Vulcans of no, there would be a lot of internal politics to overcome.
In ENT, I saw Earth (and other non-Vulcan allies) suspicious of Vulcan for both its mysterious and sometimes aggressive moves and also because it was the most technologically advanced world in the galactic neighborhood. It was stated in "Fallen Hero" that the top-of-the-line Vulcan battlecruiser could sustain Warp 7 for 15 minutes. Apparently, this became the goal of Earth (and ultimately the Coalition/Federation): to produce a new generation of starships capable of sustaining Warp 7 for at least that length of time so that a new technological plateau for advanced starships could be established for projecting power as a stabilizing influence. The would make it easier for all of the Coalition/Federation member worlds to get along and deal with any hostile neighbors. So if you're looking at the military/diplomatic aspect of it, the Coalition/Federation is going to need as many Warp 7 starships as it would take to stabilize the interstellar neighborhood and stand up credibly against any threats.
Beyond that, the backbone of any power or group of nations, today or in a speculative spacefaring future, is going to be the strength of its economy. Where does it get its raw materials from, and how are the shipped, pooled, processed, used, etc.? If the technology of the future (for everything from rail cars to computers to spacecraft) is fabricated from raw materials mined from nearby asteroids, moons, or from distant planets in other star systems (Rigel XII, Capella IV, Delta Vega), a spacefaring civilization would have to build and maintain an infrastructure of extraction, transportation, trade and manufacturing that would sustainably provide the needed gadgets, terrestrial buildings, ships, and other needed value-added goods to sustain all of the society's terrestrial communities, distant colonies and space fleets in perpetuity.
Back in 2008, I started a thread about warptugs. My supposition was that so-called "freighters" were mass-movers that acted like a cross between a railroad, a postal system and a shipping fleet. It would be the circulatory system that would sustain homeworlds, starbases, fleets, and colonies with the raw materials and processed goods they would need. We see the rudimentary references to this in the supply of quadrotriticale grain to Sherman's Planet (TOS, "The Trouble with Tribbles"; TAS, "More Tribbles, More Troubles"). I see this 2008 thread about warptugs as a kind of backbone concept for an FTL spacefaring society.
Exploratory and military starships exist for scientific, diplomatic and defensive purposes to protect and project the ongoing mission of that economy. They go out to "explore strange new worlds, to seek out new life and new civilizations" and to make sure the ongoing work of the homeworlds' / colonial economy is not disrupted.
So, if you can mine asteroids in your own home star system to provide raw materials for all of your homeworld needs, plus the needs of the Starfleet, etc., then all you need for the mining are impulse-powered ore ships. But if you need to go to Rigel XII or Delta Vega for dilithium, you'll need the build ships like the Woden or the Huron to haul your precious cargo. And ships like Huron and Woden need ships like the Enterprise to explore, research, and protect those extraction interests. (NOTE: I also recently started a different
thread on TOS and pre-TOS era freighters as well; it might also be of use.)