I personally found most of their unique ships to be extremely useful.
For mainline combat Invincible does its job perfectly, true to its name it tanks like nothing else, has decent complement of fighters and has increbidly versatile armament, the two real problems with it are extremely limited firing arcs on the turbolasers, which are basically restricted to forward only fire and kinda unimpressive shields, you build them in bulk and just park right in front of the enemy and it just works.
Recusant is pretty much a mandatory addition for every fleet, but only in moderation, serving as perfect backline support due to the extended range of the turbolaser batteries and it also doubles as anti-starfighter screening vessel due to multiple laser batteries, positioning it all the way behind your mainline sluggers and secondline fire support ships it can contribute a lot, but you still need to keep in mind that it is a vessel with precise but limited firepower, should you deploy too much of them you'll fall behind in numbers of starfighters ( as it doesn't have any ) and raw damage output.
Bulwark I is essentially a VSD II, but overall better, it doesn't have power-to-weapons, but extra bomber squad and better performance all around make it extremely good second line support.
Bulwark III is your typical high end big ship, very punchy, has some starfighters to bare and tanky as all hell, the only notable thing is that due to its position on the Z axis AI seems to ignore this ship to a certain degree.
I personally don't like Lucrehulk that much, it does spawn six bomber squads, which is extremely nice for deleting shields, but all it can do itself is wait for its bombers to their job on some poor cruiser's shields and then slowly bully it with its two quad turbolasers.
If you find yourself constantly spammed down with corvettes don't waste your money on Gladiators or Neutrons, former can't fully concentrate its firepower and latter has horrible accuracy, Dreadnoughts have pinpoint accuracy and power-to-weapons which makes them best corvette killers, adding ships with tractor beams like VSD I is the best way to ensure corvette free space.

Also want to add to Douk Nouk Kem's wonderful answer that Gozanti's and Citadel Cruisers are also very good. I haven't tried them in 2.3.1 yet but in the patch prior they were a must have. Citadel Cruisers are armed with ion cannons and Gozanti's are armed with proton torpedos, making both an excellent addition for draining shields on enemy ships.

I think my favorite frigate type ships are the neutron star and the dreadnaught. Both are reliable for what little economy you start off with. I think the Neutron star is the superior frigate for the CSA because it gives you many many bombers in the form of 2 T-wing squads and 1 Y-wing squad.

VSD's are more of a luxury until you can take Mon Calamari and build Rendili Stardrive. If you don't have Rendilit Stardrive then go the little extra mile and get the Bulwark I. Try expanding south towards Hutt space because Da Soocha, Nal Hutta, and Kessel are all planets that provide huge amounts of income if you build mining facilities/ offices/ trade ports on them. The important thing is to stay occupied in the outer rim so you don't get sandwiched by multiple factions.

I've played as the CSA on admiral. I got my economy to 7k around turn 3. Around turn 136 (year 2.8) with the CSA, I had enough momentum to take the galaxy, but had to restart due to catastrophic crashing. Gained far more planets than lost, while taking few losses in fleet battles with a major loss of only one VSD (destroyed a death squadron type fleet as an exchange).

You have to be picky about station placement and use. You have to have some planets as space defense platforms, with others with land-based defenses. Some planets will not have much defenses at all, but you must have a fleet near by to respond, retake, and push/hit and run/blockade. I usually use anywhere between 2-4 main fleets with 1-3 defense fleets.

I have a stream link to share if you would like to see and talk about the CSA.

Schedule a time and I can show how to beat this game, and I'm having fun as always with it. Ask me anything. Unfortunately, as I mentioned, the CSA save file has crashing I cannot resolve, so I'll only be able to show maybe 3 fleet battles and a land battle.

Currently I'm playing with Empire on cruel - having a blast https://www.twitch.tv/xwingjkbattlegrounds - (offline)