Recommended utility-ish mods:
Automatic Orders - lets you set ships to, for example, automatically retreat when they get close to running out of CR. All-but-mandatory if you want to use frigates or destroyers in late-game fights.
Console Commands - very useful for recovering from buggy situations - not a common problem in vanilla, but once you start adding mods there can be occasional issues. Also useful for customizing your starting fleet, though Nex also offers some decent options there too.
More Officer Skills - gives you more choices when leveling officers.
Unknown Skies - adds extra variety to planets & exploration content.
Starship Legends - adds random traits to specific ships as they do well (or poorly) in combat. (Or just at random for civilian hulls.) For me, this functions like a replacement of the old crew progression, allowing ships I've had for a while to be just a bit better than a generic hull would be.
Nexerelin is neat, but also generally makes the game harder. Has a lot of configuration options if you're willing to go messing about with its files, though, and it's possible to turn off the "player faction diplomacy" option that results in AI factions randomly becoming more hostile over time.
For general adding-of-ships, I'd suggest:
Ship & Weapon Pack
Underworld
Tahlan Shipworks
Seeker
For actual faction mods, my favorites include:
Dassault-Mikoyan Engineering
Interstellar Imperium
Blackrock Driveyards
Outer Rim Alliance
Sylphon R&D
Legacy of Arkgneisis
Diable Avionics
Shadowyards