Vanilla is no mods of any kind.
Hegemony is probably the easiest. Many trade opportunities, lots of shops and best access to rare weapons. They also have XIV ships, which are very good.
Tri-Tachyon has the best access to high-tech ships and some weapons, especially Heavy Blasters. HVDs, the best medium kinetic, are obnoxiously rare for them. Trading will be almost non-existent due to being locked out of many market, due to them owned by Hegemony. If you pick Tri-Tachyon, you will be limited mostly to fighting. If you cannot stand constant combat and limited trading, do not pick Tri-Tachyon.
Only join Sindrian Diktat if you want the Conquest very badly. Aside from Conquest, they offer nothing Hegemony does not.
Avoid Luddic Church; the sole system they control is out in a corner of nowhere. They also have no unique ships or items. (I do not think they sell Luddic Path ships, which are useless due to Ill-Advised Modifications.)
Carriers and fighters become obsolete by endgame. Even midgame, only Thunders and Daggers barely pull their weight, but once you start fighting detachments with high-level officers, fighters will simply crumple.
Frigates is where high-tech have advantage. Best are Hyperion, Tempest, Scarab, and the phase frigates. Lasher is decent for close-range fighting, and Monitor can be a decent damage sponge.
Best destroyers are Medusa and Enforcer.
Best cruisers are Dominator, Eagle, and Apogee. Falcon is decent, though it feels more like an overgrown destroyer.
Best capitals are either Paragon and Onslaught. Paragon is very easy to use, but Onslaught is the most powerful (but a bit harder to keep alive than Paragon unless you know what you are doing).
Bring some freighters if you want to trade or loot much.
Do not let burn speed fall below 9 unless you need to use an Atlas for some reason. Bring tugs if you need to.
P.S. The only way to raise reputation to Cooperative with Independents is through combat, usually by completing their named bounties.