2593. State of the universe: The civilized worlds of the Milky Way Galaxy are basically divided between the Federation (roughly 55%), the Typhon Pact (40-ish %), and the League of Independent Worlds (About 4%). The Prime Directive was greatly weakened by a series of court decisions, legislation, and regulation about 50 years ago, and decisions in the Federation government are increasingly made behind closed doors by the power elite, which seems to be dominated by Betazoids, Trill, Denobulans, and Vulcans, rather than by anything approaching a democracy or a republic. Senior ranks in Starfleet are also increasingly dominated by those four species, especially in positions that control actual military force - the only human in command of any of the two most powerful classes of vessels is Commodore Sara Chandler of the USS Triumphant.
Andor left the Federation 10 years ago and is in talks to join the Typhon Pact, which from an outside view, has become a better alternative for individual liberties and rights than the Federation, though this would be scoffed at by most inside the Federation, who still talk their standard, traditional lines about peace and cooperation and the subtle positions that imply human cultural and moral superiority and a galactic manifest destiny. The Borg joined the Federation, making large concessions in their mode of operations in order to secure Federation assistance against a much larger threat the entire galaxy is facing.
Now, the ships, from biggest to smallest:
Farship - Aurora-Class - utilizing technologies from many Federation contributors, but mainly from the Borg and the Voth, these are huge, mostly spherical mobile starbases, diplomatic, exploration, and colonization platforms, large enough to hold 72 starships of Excelsior-class or smaller, plus many, many more shuttles, workbees, fighters, and other support ships, a standard crew complement of around 8,000, and a volunteer civilian population numbering in the tens of thousands who are housed in a large civilian area that even has its own city government for internal matters. Reasonably well-armed and shielded (comparable to late-season DS9), but mostly relies on starship support and its ability to bug out quickly for defense. One of only two types of vessels outfitted with Sidewarp Drive, capable of transporting the ship across vast, intergalactic distances very rapidly (3 weeks to Andromeda). 3 have been constructed and launched - USS Aurora, USS Origin, and USS Unimatrix. Contact has been lost with Origin, she is feared lost, and construction of additional Farships is in review to attempt to determine the cause and prevent future occurrences. Command of a Farship is given to a member of senior Admiralty with extensive experience commanding starships AND administrating starbases.
EPPs ("Enhanced Projection Platforms", because it sounds more subtle and in line with Federation principles than Superdreadnought) - Indomitable-Class - armed to the teeth with a standard crew complement of over 5,000 and two shuttlebays each capable of docking one of the old Constitution-Class starships if they were emptied of their usual complements of shuttles, fighters, workbees, etc. Outfitted with two Slipstream nacelles, two (experimental, smaller) Sidewarp engines, and two *additional* inboard Slipstream nacelles on the saucer section. Mission profiles include transport of high ranking Federation officials when travelling to potentially risky places, courier and support runs for Farships, border patrol in heavily contested regions, and visiting member worlds that are thinking of leaving the Federation to show them how important they are (and if they also happen to be a bit intimidated, that works, too). There are 13 in service (a number chosen as part of honoring the Enterprise name - which shows you how deeply the politics goes into decision making), including USS Indomitable (NCC-170101), USS Triumphant (NCC-170110), and USS Enterprise (NCC-170100 - out of sequence but held for the Enterprise). Command of a Superdreadnaught is given to a Rear Admiral, but convention has again come to be to refer to a Rear Admiral in command of a starship or starbase as "Commodore". The Executive Officer billet is a Flag Captain's assignment, and these ships have a dual-deck bridge with an upper deck for fleet command and a lower deck for local ship command.
PPs ("Projection Platforms", NOT "Dreadnoughts"

) - a variety of classes built with the primary purposes of defense/battle and border patrol. Heavy automation and limited mission profiles mean that standard crew complements are generally low - 150 is typical. These are the billets of Flag Captains - captains who have seniority and would potentially be assigned to command task groups.
Explorer - a variety of classes built for exploration and for performing research and other functions in areas where contention might be anticipated, such as defending an outpost while under construction, making adjustments to border sensor arrays, anti-piracy operations, troop transport, and analyzing spatial anomalies near Andor. Moderately armed, armored, and shielded - three of these would be considered approximately a fair fight against a PP. Standard crew complement is generally 500-1000, but can rise as high as 4,000 depending on specific class and mission profile.These are generally the billets of Captains with a previous ship command under their belt.
Cruiser - a variety of classes (including the venerable Excelsior-class, STILL, downrated from its old Heavy Cruiser role and refit again) that serve as the workhorses of the Federation: research and sensor data updates well inside Federation borders, internal transport of important people, tractor recovery of disabled starships and space transports, customs and ship inspection, and primary system defense forces. Generally, standard crew complement is 150-200, but can rise as high as 750 depending on specific class and mission profile. These are the billets of new Captains or, occasionally, a Commander whose star is rising quickly.
Escort - a variety of classes built to act as armed escorts for larger vessels, both Starfleet and otherwise (colony ships, transports, Farships, task groups, ships transporting important personages, etc). Small, but heavily armed and armored and very maneuverable, with crew complements generally under 80. These are the billets of Commanders and occasionally, Lt. Commanders.
Transports/Carriers - a handful of classes built to maximize internal volume to act as hospital ships, troop transports, cargo transports for sensitive cargo, fighter craft, etc. Very large vessels, but minimal armaments and crew - though they are usually outfitted with decent to superior armor and shielding. Hospital variants can be the billet of anyone who has passed Starfleet Command Training, which is usually (but not always) at least a Lt. Commander. Troop transport command is often assigned as a mission, when need for such transport arises, and generally to an officer that outranks the troops they will be carrying - such ships are generally used for cargo when not pressed into service for troop transport. Fighter carriers are usually the billet of a Captain or Flag Captain with previous starship command experience, and their exec is generally also a Captain - the Wing Commander for the fighter complement. And a cargo transport can be commanded by any commissioned officer, even an Ensign (although it would be considered an unusual honor for an Ensign to be given a command billet, intended by a senior officer to accelerate their later career), as the crew is generally non-commissioned, and no flag decisions are expected to be required.