Personally i think carrier based fleets are the most powerful kind of fleets you can field. Of course a good player with its flagship will always be better but i think fighters are more viable than other ships because they are basically "immortals" thanks to their carrier.
I prefere low-tech fleets as high-tech toys are very expensive and not that good. Tridents are pretty bad, longbows are horrendous (you can try the Starsector+ mod, they are better balanced). Wasps, while they are excellent interceptors, that's the only thing they can do effectively. Xyphos are pretty good but cost way too much to be cost effective, also they are big targets. The Dagger is perhaps the only very good high-tech craft that you will find, 3 reapers in the enemy's face never disappoint.
Low tech fighters are much more handy in my opinion. The Talon is dirt cheap, it's a decent interceptor, it's fast, its vulcan will rip open shields and tear the hull of bigger ships, they are the perfect cannon fodder for your fleet. The Broadsword is basically a bigger, fatter Talon but it's also more expensive. Definitely a good fighter early on but i tend to prefer the more "swarmy" Talon for end game fleets.
Fewer armored fighters however have the advantage of losing much less crafts in battle, resulting in less supply cost. If you prefer fewer but stronger crafts, the Gladius is a good bet, it's tough as nail and the dual IR pulse can tear through anything. Not the best Interceptor though. The Warthog is even tankier and its LAG make it very good against low-tech vessels that lack shields. Unfortunately they are horribly slow and will get distanced by the rest of your fighters, keeping tight formations is really important to avoid the focus fire of enemy PDs.
The Thunder is one of the most important fighter for any fleet. Early game its single harpoon make it a decent bomber against frigates and destroyers. What make the Thunder awesome is its incredible speed, making chasing scenarios and capturing strategic points very easy. The ion cannon will also make sure that any big ship won't be able to use their full firepower and hamper their mobility. Not your core fighter but the most important support craft of your fleet.
Piranhas are pretty bad early on because they are slow and can't properly hit with their bomb bays. Later however they are probably the best bomber available. They are though, bomb bays hurt like trucks and you can field a lot of them. Hitting a destroyer can be difficult but a cruiser or a capital ship usually can't escape the first wave of Piranha bombing.
Mining drones are civilians ships, they don't have their place on the battlefield.
For the carriers, the Gemini is the king. It's cheap, it can provide long range support with Pilums lrms, it have a nice cargo capacity, PD drones plus 2 mediums mounts for flaks prevent enemy fighters from reaching it. It's pretty beastly. The Condor isn't bad either but the Gemini is just too good.
In the cruiser category, the Heron is also a very good choice for a "pure" carrier. If you feel like playing less passive, the Venture is a decent battle carrier too, not as efficient at resupplying your fighter though. Going to the front line is also a big risk as losing a carrier is a huge blow to your fleet.
I pretty much never use capital carriers, way too expensive for my taste. The Astral, while it have 6 launch bays, will also probably be the sole carrier in your fleet, losing it equal defeat. It's atrociously slow too.
For the skills, getting 5 points in mechanical engineering will grant 10% hull for your fleet, very useful, the additional OPs help your carriers too. Construction is very good if you use a lot of low-tech ships as they mainly use armor and the boost granted by the Construction skill is very powerful. Navigation skill is always needed, no matter what kind of fleet you need.
Leadership skill is obviously the most important, maxing fleet logistic is what make a carrier fleet scary. You can also skill command experience, at 10 points your unlock the juicy "making do" perk, which will reduce tremendously the supply cost of your fleet, very expensive to get though.
Also a trick that you should use, always place your carriers at the bottom in your fleet screen. Carriers don't benefit much from the experienced crew, fighters does. An elite crewed Talon will always be better than a regular crewed one. You don't need Aces to fire those Pilums anyway.
Edit: Mega text wall of doom!