I've gotten Miranda, Intrepid, Excelsior, California, and Defiant-classes. the last Borg related mission says something about having a number of Sovereign-class, so I image we get those at some point.
A lot of the missions are front loaded so you need to get through a bunch of stuff in the first 50 years (when Romulus explodes). In Stellaris, you don't really get to the larger ships until you are over a hundred years into the game. Miranda seem to translate to Destroyer. Intrepid as a Cruiser. Defiant comes with the upgrade of the Enterprise to the 1701-E, and seems like a Corvette sized ships with a kick. Excelsior seems to be the Battleship, so I image the Sovereign is the Titan-class.
Star Trek: Infinite's Victory screen shows that the game (on default) will end in the year 2646. So three hundred years after the start of the game. Last I played I was in I think the year 2411, or so, and pretty much explored every star system, but it will take a long time to expand into all of that. I did notice that there are some stars away off near the edges of the map. The anomalies are not in the same place every time, and I think the minor powers are in different places aside from the starting ones that each major power is expected to interact with from turn one.
The hardest part for me so far has been Bajor. Liberating it seems to be an issue if you let Cardassia absorb it (which I thought would have started a way if they went to integrate...I was wrong). I did get into a war with myself allied to the Romulas against both the Cardassians and Klingons, but I didn't have enough Influence to claim Bajor (needed something like 280 Influence for just the one system). And because the Federation can only fight defensive wars, I can't claim the system outside of a war....so how am I suppose to get Bajor liberated now? I got another two hundred years, so maybe another war will happen...its just that with all the systems still needing to be taken, it will be hard to keep 300 or so Influence handy just for Bajor (Stellaris has Influence for claims down a lot lower...also for just taking systems. The lowest I've seen is 86 Influence, with some systems being 103 or 120 without might difference. I've not quite gotten use to how the warp ranges function in relation to starbases and if that can be upgraded with upgraded starbases or not. I know there is tech that will increase ranges, but it seems like I have a lot of tech to go through still.
I image there will be DLC and mods that add the other quadrants (and powers, mostly from the Delta Quadrant since we saw more of those on Voyager's trip, while the Gamma Quadrant has basically just the Dominion). I don't think you will be the Borg at any point (unless you are the Crisis). But I could see someone modding the game into the 2140s or 2240s starting period, or even a Kelvinverse version starting in 2233 with Nero's entry and the destruction of the USS Kelvin in place of the Khitomer Massacre. For the 2140s, there could either be more major powers, or you could be just about any minor power, as Earth, Vulcan, Andor, Tellar, would all be minor powers. The NX-01 Enterprise would be the mission for Earth in that era. For the 2240s, the Major powers could replace Cardassia with ther Gorn Hegemony, and the NCC-1701 Enterprise would be the mission, Either with Pike's Crew or Kirk's Crew, or have that even be an upgrade path of the Enterprises.