Carrier questions you say? I can do these. Since it's what I fly. Well.. carriers anyway and being a KDF main... well... you get the point.
Well, not going to lie. You potential cat carriers got some work ahead of you. It's the weakest of all the carriers, but it can still be a lot of fun. You just have to do some work and have an idea of how you want to approach things.
The first is to decide your playstyle and weapon loadout. Cat Carrier -can- use cannons... but this is going to force you to use RCS Movement consoles somewhere.. and even with a lot of them.. because of the poor turn rate.. even getting 4 of them can make things.... not much better. It's got a 5 and I remember 4 RCS only boosted me to 4.5 So.. you'd likely want to use something else. That means beams.
If you can play the ship as a mobile blockade fortress, it works well. Broadside and powerslide into a nice place. Park, and just fire all those beams. You'll do a nice amount of contribution. Just beware you'll likely be using Evasive Maneuvers as a turning buff. So pick your favorite damage type and go with that. I would also recommend a borg cutting beam in the back. If you happen to use Anti-Proton, the 360 beam array will be a good choice for the backslot until you get more comfortable broadsiding.
The reason I have to recommend beams on the cat carrier is due to the Lt Tac spot. There's not really much you can do with it. It's really either Heavy Yield 1, Torp Spread 1 or Tac Team 1 as the first spot. You run a primary torp spot, but even running a Borg cutting beam, 360 beam array, you still lose out on either the torpedo spot or a back beam array. Plus Tac Team is so valuable and once you get aggro (You will if you're built right), the shield modulation helps so much.
With your second slot, I'd likely say fire all beams. Get all of those arrays going crazy enjoy the blasts. Also, you could go Tac team 1 and Tac 2 if you want less offense and more personal defense. But in it's current state beam array fire at will is likely the better candidate for getting higher spots on DPS scoreboards, thus getting better rewards.
For your tact consoles, I always recommend no matter what, matching damage types. So get either something that boosts your chosen weapon damage type, or get crit chance damage boosting consoles. As for what damage type. Use whatever you enjoy, but I will say Disruptor and Romulan Plasma have the best synergy to go along with your pets (which we will discuss near the end.)
With your glaring weakness out of the way, we can hit up Engineering. Which is decent. You got an Lt Commander spot and 3 console spots. Your hull isn't as good as a Vo'Quz, but least it's decent. Personally, I'd run something like Emergency Power to Shields 1 and 2. Then Emergency Power to Aux. They share the same cooldown, which I dislike, but EMP to Aux can help boost your sci powers which is your strongest aspect and where your ship can shine. One of the Emergency Powers to Shields can also be dropped for Aux to Structural Integrity if you're feeling you're taking too much hull bleed through. But really that should be covered. We'll cover console stuff later.
The good stuff. We're on science. This is where the ship shines, and you need to play to it's strengths. You have one Cmd Science and an Lt Cmd. Your CMD science should, as it's fourth ability. Gravity Well 3. Trust me. This power hits as hard as lance type powers (like the Garumba and Vesta). Boosting your aux right before you throw this off will toss on some delicious damage, as well as yanking everything in sight. If you're not a science officer, you'll need someone to train your boffs in it. Also, the reward for Tier 5 Dyson gives you a bridge officer with it. For your next to final, I'd also throw in Gravity Well 2. It's really the best CC in the game. The damage from 2 isn't as nice as GW3, but it's great to have it as an option with double the up time.
As for the opening slots. Hazard Emitters 1 or 2 and Transfer Shield Strength 1 and 2 are wonderful. Good healing on the hull, good shield regen, wipe out those annoying plasma fires the borg loves... but also you can throw them onto other teammates you don't want to see die. So group friendly as well. Which would leave an entire officer up to you. The Lt Cmd science. You could run copies of both HE and TSS to help yourself and give you more of an undying zombie. Your other options largely depend on how you are skill build. The suggestions I made really also assume a very standard any class fits all build where everyone should have their shield heals maxed, along with their hull repair skills. The last boff could really just double down on what you have if you don't have skills like Viral Matrix to really capitalize on. (If your needed skills aren't boosted, it's better not to have it at all). I avoid science team just cause it forces the cooldown on Tac team. That is an option if you wanted to avoid tac team as well.. but.. tac team would do more.
Consoles / Sets / Gear.
Plasmonic Leech. Get it. Enjoy it. Let your beams have much more energy then they need. If you don't have the cash.. the MACO Shield will excellent as well in it's place. But never both of these. They interact wonky with one another.
If you're going to use beams, Nukara particle Gen from the Nukara Rep is an excellent console. 10% beam accuracy? Delicious.
Assimilated Console + Zero Point Console. I'd recommend these as well. Your beams will be doing much more DPS then you could imagine.
You could also test to see if you think RCS are your thing. I thought they didn't help much due to the initial turn rate. However if you use plasma or romulan plasma as your weapon type, embassy plasma consoles could not only boost your GW3 damage, but also your initial plasma damage. Get some that reduce threat generation. These consoles are stupidly good which makes Rom Plasma the best weapon type in the game if you got the overpriced dilithum to buy them with. But you'd also need not many.. so it works out. Plus with 4 of them.. you could boost your damage up by about 40%.. with your 2 tac consoles... giving you around over 100% and more. It's good.
The ship can easily function with any set. So enjoy that. Though Dyson set is likely the weakest, even if you do boost your sci numbers. That shield is just too weak. But it's better then say random whites / blues. So usual set rules applies:
Borg if you need survivability, Maco if you don't got the leech, elite fleet shields + whatever if you do.
So that brings us to the last part.. and this is the most important. You're only going to be as good as your beautiful pets. Earlier I mentioned that this is the weakest carrier in the game. Sadly, this is partially why. The biggest weakness is the ship's inability to equip frigate type ships. Fighters die. Fast. Probably because they, or you, or even your team did their job. It's unfortunate.. but the other issue lies in that their exclusive ship, the stalker fighters are dreadfully awful. At least until Elite Stalkers. Then things change... sorta. Let's get the basics out of the way.
Your goal, no matter what on your carriers are to get your elite pets. Which ones you want, are up to you. I can give you some suggestions but keep in mind the price. You're looking at on average:
100,000 Fleet Credits and 50k Dilithium PER hanger pet. You're going to need two elite pets. That's a lot. And unfortunately many of the main federation pet types just aren't that good. Do not ever waste your money and time on Type 8's and their upgrade type 10's. No. Do not. They are a trap and one of the worst wastes of your resources on pets.
Your danbue / yellowstone on the other hand is an excellent decision on pets if you feel you need more control. But that's all they really do. They have some decent DPS, but their main feature is control. They are a good investment if you feel you lack control or want to have annoying spam pets.
Delta Fliers are a personal taste. They're decent on shield targets due to their transphasic torpedos but... after that.. and when the shields are down... They're outperformed. Are they terrible? Thankfully no. But they have their place.
The last of the federation made ships would be the Peregrine. They're fighters who do exactly that. They fight, they do it well. If you want a DPS pet, but don't want to do reputation for scoprions or you want to say RP all federation only type of things. This is your choice. Do they parse well though? While their DPS is good, do note, they're not even in the top 5 for damage.
Your special ship, like I had mentioned earlier, Elite Stalkers. These are good compared to their blue and advanced versions. (Don't buy the advanced versions.) But they're very specialized. They're pure shield strippers, however other shield stripping ships do it better. No one would groan seeing you with elites like they would type 8's or 10s. But much like shield striping attacks are.. after the fact they're a bit lacking. Mix and matching with elite scorpions has some potential.
Elite Swarmers. These little buggers are nice. You can't use the freebies from the Featured Episode, however if you buy the ones from the Spire Store, they can go onto other ship. They have some very excellent burst. But then will probably blow up. They felt weaker to me then some fighters as survivability. So AoE heavy foes can be extra scary. (Voth). They also have BO3. Ywouch. They're easily recommendable. But again if you're min-maxing. They're not your pet of choice.
Elite Tholian Widow. Now, these are the better version of Stalker Fighters. They're only acquirable however with T5 Nukara Rep. So while they will be cheaper FC wise and a bit cheaper ore.. they require 30 white doffs of ops and engineering I think. Something like that. Maybe more, it's been awhile. They were formerly exclusive for the Recluse, but they were given Mesh Weavers instead. These guys hit hard, strip shields, and pack torpedos. Plus they have fire all beams so it goes everywhere. However.. they waste an ability slot on something that only the Recluse gets. Which is 33% bonus to damage for way too long of a CD. But if you like tholian style ships.. here you go.
Elite Scoprion Fighters. The former king of pets. But still in the top five of all time pets. You ever been in an STF with a guy with Romulan Torpedos? And you can tell he's got the torpedo doff cause there's 249329429492 torpedos on the screen? Yeah. This is what they do also. Not as much, but if you're running 2 sets... that's 12 fighters all spamming high yield plasma 1. Even if they die fast, you can relaunch them and they'll have fresh torpedo spam ready to go. Not to mention their blasts are good. They are like the tholians where you can only get them with T5 Romulan Reputation and they cost a lot of doffs and around 30k-ish dilithium. If you're looking to squeeze out even more crazy DPS. Here you go. Things to note, that these guys can parse better then poor players. HOWEVER. They have a weakness to AoE (All fighters do) but, it's worth extra mentioning because their torpedo are targetable.. if they start introducing mobs that gravity well players more... their dps will drop fast. Cause it's all based on the massive torpedo damage.
Bonus Round -
If you're seriously wanting to main carriers, I'd HIGHLY recommend you to pick up the lockbox trait Wing Commander. Will run around 10-20 million, but it cuts down the experience needed for your pets to level up by half. You may actually see your fighters get to rank 5, vs the chance of them surviving that long... is hard.
Also, if you've got the money or lobi and want a better version of the Cat Carrier. Grab a Recluse for around 80 million or 800 lobi. Get access to Frigate Pets, and one of the best ships in the game. Turns better, has more universal slots so you can fine tune it. Easily one of the best carriers in the game.
Finally, I'm not sure if I mentioned it. But I also have to stress. Save your money, resources and dilithium for the elite versions of the pet of your choice. Do not waste it on advanced versions. All the reviews of the pets I gave as for the elite. The advanced on many of them, are awful. Advanced Scoprions don't come anywhere close due to their high yield. And the blue widows / scoprions still want a stupid amount of doffs. You can run peregrine or dunabe's, or any ship just fine until you get the cost or reputations leveled for the elite. Trust me on this.