Keep in mind that these are mostly based on my experiences, so feel free to experiment and tweak it as it works for you.
I set each ship to escort each other, and form on me. No one goes off on their own. What usually plays out, we face off with enemy and they eventually overwhelm us. They also have mostly cruisers, destroyers and frigates. My heavy firepower onslaught and his supporting cruisers and destroyers make no difference.
In the beginning, I used to do that but you have to realize what the escort order does. Currently the escort order does not mean 'follow this ship and provide backup' it means 'Put yourself between the enemies bullets and this ship regardless of size differences' with the exception of carriers who prefer to hide behind escort targets.
Instead, don't be afraid to let ships be free roaming. Though this does mean checking up every so often to ensure no one gets into an overextended position with no chance of rescue (though orders as suggestions can prevent you saving them anyway) the ships on your team tend to be very cautious and conservative in what they do and will more often than not be perfectly fine on their own. This is more true the bigger ships you have in your fleet as larger ships are not able to travel quickly and so will be more likely to fight around allies in a line whereas frigates will usually zip around and wind up behind enemy lines either skirmishing or kiting.
Also, escort does not work well between ships that have wildly different speeds as a slower vessel can't keep up with a really quick one so they won't support each other and a quick one won't use its superior speed to stay safe because of the leash the escort order gives it.
I try to fit with variation of anti shields and anti armor weapons on my battleship which I fly. I never had any trouble getting this far, I mean I'd say im in mid-end game area now, I've won lots of battles during that time. Should I be trying to out maneuver people instead of getting in a shooting war? Are my weapons terrible?
Depends on what kind of ship you're piloting and what you like to do. Are you flying a Hyperion, tempest, or Aurora? Go around the flank and hammer anything that overextends itself or backs off while weakened from your main line.
Playing as a Paragon, onslaught, hammerhead, or SO lasher in the earlier game? Fly in there and cause some trouble with your superior firepower. Don't be afraid to do a head on approach when flying an onslaught as excluding mods, stations, and remnants it has the highest offensive power of all sector ships.
If you desire to be a Heron or Astral then make sure to take things in a more tactical manner and more actively directing your fighters and fleet to achieve your goals.
I will say though that how you build your ships will have the largest impact on their performance, which is why Loadout Design 3 is considered on of the top tier skills in the game. What you want to do is try to think of a role for the ship to do and build for it, and very importantly make sure that what you hand off to the AI is something that they'll be able to make good use of. The AI are very good at being a line, but don't expect it to smartly use a quick, high alpha damage, assassin style ship as that's more the player's territory. Don't feel as though you have to fulfill that role though, there are many ways to skin a cat in this game.
What are some good suggestions for fighters/bombers to use on my 4 carriers?
Depends on what your carriers are and what you want to do with them.
For general bombing runs I would suggest a mixture of Broadswords/Longbows(Anti-shield/Torpedo protection) + Daggers/Perditions/Khopesh/Tridents(Anti-armor/hull)
For fighter superiority you can go with a lot of sparks/wasps/xyphos/thunders
For anti-frigate flankers any fighter with excellent speed and a high range of engagement such as thunders(ion suppression, but takes awhile) + gladius(can bring more damage than thunders)
For destroying starbases, Piranhas, which are normally horrible in fights due to always missing or friendly fire threats, can be very dangerous in raw damage output and PD saturation on the stationary target.
Also, coming up against a fleet of equal size and strength one must expect to take losses, but even losing 3-4 ships an engagement is crippling money wise. And then there is no point recovering them even if they are intact because of the permanent damage to them.
Don't be afraid to recover ships just because they have some D-mods. The D-mods even make ships cheaper to deploy in fights making them cost less in supplies to fight, and if you really want to there's a skill that reduces ships' maintenance costs based on its D-mods.
You don't need to restore the ship and in-fact I advise against it as its cheaper to manufacture or buy a new one. Restore is there for extremely rare/unique ships that you cannot easily replace with the earlier two methods.
D-mods mean far less than outnumbering your opponents, so long as they're not something crippling such as degraded engines(Can reduce fleet burn speed which can be dangerous for your fleet.), any D-mod that affects fighters for a carrier(means fighters will die quickly and uselessly), or damaged cargo bays for freighters.
In-addition to that don't be afraid to not only recover your own ships, but feel free to recover enemy ships as well if they're worthy.
Also, should I lean heavy to flux cap or flux vents? I max out both. I see people lean heavy towards vents and less flux cap, and just leave off some weapons to put on more system mods.
Generally vents over caps, with some exceptions where more caps are better and vent speed doesn't matter (ie. Phase ships, frigates, hyperion). I will say though that if you're regularly spending enough OP to max out both weapons and flux stats that you should think about using more Hullmods. Many hullmods can be extremely good, like expanded missile rack can make double the reapers effectively doubling how many cruisers can be immediately put out of commission and Integrated Targeting Unit is a staple of almost every warship build type with Expanded Deck Crew being its Carrier must-have version.
Don't be afraid to leave some weapon slots empty too to help with a ship's flux stats or to get more OP to assist the build plan you're going for on a ship. A scarab is a good example of a ship that benefits heavily from leaving some weapon slots empty.