So, she's probably the one that picked the Intrepid and Akira designs too. Also, the Nova-class itself is actually not that bad for what it is. Yes, it is an Oberth replacement and thus, is undergunned even by the standards of 2370s Starfleet, but considering Ransom was able to keep that ship around for 5 years without Starbase support, that proves it's actually a solid design for most purposes.
Maybe I am too military minded for Starfleet, but if I had a say in there, I'd very likely scrap most ship classes, even things like the Nova or Steamrunner. Instead I'd settle on a very tiny amount of classes that are optimised for mass production, simplified logistics and maintenance and a certain room for future upgrades. Pretty much what Starfleet DID with the Constitution and Excelsior classes in the 23rd century. And I wouldn't do it solely for the reason that I anticipate large scale warefare. It's simply much more economical.
So, you have for instance a modularised Intrepid that in this version of 2370ish Starfleet also is the smallest ship and which you can use as a mobile science lab as well - with all science shit swapped for phasers - a convoy escort, picket ship, destroyer/torpedo boat or patrol. The next largest thing would be the Lakota-subtype of the Excelsior, you know, the ship Leyton used. The role would be still the same for this as for the original Excelsiors. Why would I keep them around? Well, it's a very sound base design that you can refit to serve various purposes: destroyer leader/light cruiser, fast heavy escort, exploration vessel for first contact stuff.
Next is the Galaxy-class. Well, decent enough design -provided the kinks are fixed, which Starfleet eventually indeed did. Man, I'd give it a whole lot more phaser arrays and torpedo tubes. Like, they gave the original blueprint TWO torpedo tubes. FUCKING TWO! How about a dozen? Or add that big ass long range, hart hitting, super sniper-phaser cannon the X-type had in All Good Things? Seriously, if the mission profile states that the Galaxy has to go out there alone for a long time, you wanna have some quite tough tactical systems. In particular if one of the intended mission profiles is all about serving as a flagship, of all things.
I'd keep the Nebulas, largely to serve as general purpose support ships. You could configure them for electronic warfare and add as many sensors and jammers you can find. You also could use them as resupply ships, flying gas stations, essentially. Or how about as squad leaders for your Intrepid/Excelsior escorts. Or mobile com relay platforms.
Then there's the Sovereign. Well, no complaints here. They finally built something that actually does work from day one.
That would be the core, but there is a need to fight something like a Borg-cube without getting plastered with all the cutting beams in the universe. So, that means a lot of staying power. And a whole plethora of long range weaponry that have enough punch to penetrate hundreds of meters worth of the cube without the Borg being able to adapt immediately. That means a spinal mount particle beam. That means a very large, probably elongated hull. That means a lot of powerplants. I mean, such a ship wouldn't only be useful to pin down Borg cubes, but also as a long-range siege weapon that can snipe at Dominion/Cardassian shipyards and starbases without getting too much punishment in return. For something like this I'd probably even consider large calibre railguns as an alternative to directed energy weapons. I don't know how well ships are protected against metal slugs that come in at considerable fractions of lightspeed.
Also, fuck the Romulans. Install cloaks on all ships. Reinstate Pressman to finish the transphasic cloak.