I'm not sure if you want to dive into "niche" roles or not, since I know you're taking more of an
Age of Empires or stock-
Armada II approach to Yesteryears, for example - but if you wanted a more complex sort of equation (which would admittedly take a bit more work, not least in terms of balancing), you could add in things like artillery ships, troop transports, multi-targeting gunships, torpedo cruisers, fighter carriers, fleet tenders, spaceborne sensor platforms, and/or warp interdictors.
If you decide to include the
New Orleans-class, for instance, a good role for it might be as artillery ship, or as torpedo cruiser. Personally, I like the
Akira-class as a torpedo cruiser. The
Steamrunner-class could be used in its stock role as an artillery ship, if you so desired. I believe AoW used the
Norway-class as a Federation artillery ship. Owing to the ****py quality of the stock
Iwo Jima-class, it is always open to redesign if you thought it'd be a good Federation troopship, or another design could be used. The
Steamrunner- or
Achilles-class could both be used pretty effectively in the role, I figure. Certainly the
Curry-class was designed to be a fighter carrier, and as you said, it was seen in that role in DS9. The
Apollo-class, should you include it, looks the part of a sensor platform, as does the
Phoenix-type of the
Nebula-class. A refit of the
Miranda-class to carry repair beam technology as a fleet tender might be interesting, or an entirely different class of ship. We never really saw the Federation using multi-targeting or warp-interdicting technology, at least not in the Dominion War, but if you wanted to include those somehow, they could be made to fit, I'm sure
Brief thoughts on other races: don't see Klingons caring much for artillery ships or fleet tenders, don't see Romulans employing dedicated torpedo cruisers or fighter carriers, can't imagine Cardassians coming up with the technology for spaceborne sensor platforms or warp interdictors, don't really see the Dominion being overly concerned with fleet tenders or fighter carriers (unless a Dreadnought could launch bugships...), and doubt the reclusive Breen would build troop transports or multi-targeting gunships. As for the Remans and Son'a, I'm really not sure.
Just some thoughts, YMMV