Most mods now require
Lazylibs and
Shaderlib to properly work, so use them. I you don't have a very good computer, i recommend you using Shaderlib basic edition. Also you might need to modify your vmparams files to avoid some saving/loading problems (explanation on the Uomoz mod front page)
For the mods themselves,
Ironclads is probably the oldest Total conversion and without a doubt the most complete. If you want something a bit different than Starsector.
Uomoz's sector isn't a total conversion but it change quite a bit the gameplay. Supplies are much more expensive and nearly everyone will want your blood, in some way it feel like a Pirate simulator. If you have some trouble playing the original Starsector game, i don't recommend you this mod, it's hard as nail.
Starsector + is a mod that re-balance some elements of the original game, add some new ships and weapons and properly integrate other factions mod. It's pretty much the same as the original Starsector, just with more stuffs. You'll have to separately download other factions to have them in game though.
Blackrock Drive Yards is probably one of the most popular mod faction on the forum and for good reasons. BRDY is a high-tech faction with an emphasis on high mobility and powerful alpha strikes.
Exigency Incorporated is another high-tech faction that rely on their weird technology (no shields, they use repulsors fields instead) and are very good at slowly grinding the enemy fleet to death with their missile spam. They are probably one of the weirdest faction to play and may appear weak at first glance.
Interstellar Imperium is a mid-tech faction with extremely slow and sturdy ships that rely on long range fight, they also have cruiser sized missiles.
The Knights Templars are a very high-tech NPC faction that fill the role of end-game boss. It's usually best to ignore them until you amass a fleet that can steamroll without too much effort the Hegemony system defense fleet.
The Junk Pirates are a low-tech faction, probably one of the oldest faction mod in the forum. They play very similarly to the vanilla pirates ships.
Shadowyards Heavy Industries is a high-tech faction with a wide variety of ships for every roles. They play a bit like the Tri-tachyons from the original game with more fancy tricks.
The Mayorate is a mid/high-tech faction that work in a similar way to Blackrock with good mobility and lot of guns.
SCY is a mid-tech pseudo-pirate faction. They rely on their good mobility and extreme firepower. They have paper armor though and if they can't kill their target quickly, they're in big trouble. They also have a lot of funky weapons.
Tore Up Plenty is a mod that add a wide variety of different ships, most of them are modified variants from vanilla ships. Have a clear emphasis on low-tech crafts.
Neutrino corp is a very high-tech faction with very powerful (and expensive) ships. One of Neutrino's trademark is their extremely strong but small shield. Have been considered overpowered for a while.
Citadel is a mid/high-tech mercenary faction with efficient and fast ships. A bit expensive though.
PACK is a low-tech faction with inexpensive, smaller ships. As their name suggest, they become much more dangerous in large group.
Project Valkyrie is a mid-tech faction that emphasize on slow, giant, over-armed ships. Considered a bit overpowered though.
The Gedune is a faction with med/high-tech ships with smaller ships but good mobility and pretty brutal firepower. Currently their station doesn't sell their own ships so they are more like a NPC faction.
The Nomads are a low-tech faction with mostly built-in weapons. Their ships are some of the best close range brawlers in the game, a bit too strong maybe.
I volunterly forgot some factions (P9, Thule Legacy...) are they are currently in a non-playable state. Otherwise, here some very useful utility mod.
Common radar mod that add a radar in combat and in the campaign screen.
Omnifactory is a very useful mod that add a green station in Corvus. When you drop weapons and ships in it, it will disassemble them and will start producing those. Very good when you want to mass-produce some specific ships.