The current SS (and thus mod) version is 0.65.2a. Mods not updated to .65.1a won't work due to the big campaign sorta-rewrite/trade system addition breaking tons of stuff. Also, you generally
need 64-bit java and at least 2 gb of ram available. Outside of small cases like using very few mods or playing unmodded, this is unavoidable and you might as well read that link first. (I'd recommend Alternative B for simplicity if you can locate your jre7 folder, since that way you can use the launcher the installation shortcut is already setup to open)
Utilities:
LazyLib: Its a utility library. Will save lots of effort if you just leave this enabled all the time, since a major portion of the mods use it to some degree.
ShaderLib: Fanciness, if the mod is supporting it. (stuff like shield ripples on impact) Can be configured to not display its fanciness if your comp can't handle it while still being there for the sake of mod dependancy. Not nearly as important as Lazylib, but by the same wizard.
Common Radar: Gives you a nifty radar in the corner, if you add it into your game. Shouldn't break saves, I'd expect.
Leading pip: Helps you aim weapons that would actually need aim. Not perfect, but good enough. Starsector+ has a version of this builtin to a high-level skill, otherwise its identical to the Radar in safety.
Console Commands: Its a console. You can cheat with it if you want, or you can just have this so the semi-updated
skill-respec mod is available to you.
Version Checker: It checks mod versions. And SS versions. Not required by anything, not really important if you pay attention to the mods forum, but convenient otherwise.
Omnifactory: Not actually a utility (you can set it to several settings ranging from 'replicate ships or weapons for free, time not counting' to 'Replicate ships/weapons but require paying roughly 70% more than from the faction itself' to 'Replicate ships/weapons, but only if you give it enough crew or supplies or fuel, and you may or may not have to pay for them as well'), but certainly something I'd prefer to have on hand in the background. By default it will spawn in a random, unused spot in a random system in the sector, but you can turn that off. if you do, when the game is started instead it will spawn orbiting the planet formerly named Corvus V. If you sell it weapons or ships, it will tear them down and rebuild them for you, so even if your favored faction's station(s) do not have that ship for sale at the moment, as long as the omnifactory has been given one there will be at least one available to buy, given enough time. Colored in the player-faction color, as it is not part of the Independants but is as neutral as the swiss otherwise.
Big mods:
Project Ironclads: A total conversion mod, which means that only utility mods will work alongside it (everything else will get unselected anyway, but its worth noting) Haven't played it myself, but since Vacuum hasn't updated in a long time, this is the only TC I know of for the recent version.
Starsector+ (this link is also for any of the mods mentioned in its OP except lazylib/shaderlib): Not a total conversion mod, but it does modify vanilla parts slightly, as the name probably suggests. Adds a few features, generally is a bit harder than vanilla, should work with basically any of the other mods, though only the ones actually mentioned in its post will make use of the extra features. Other mods will act as if those extras didn't exist and continue as normal.
Knights Templar: Requires SS+ to even work. "A great deal of magical hax and shaders and coding wizardry." describes them well. Intended as a boss faction for people who run out of other things to challenge. Very effective ships if you manage to capture one (or gain their favor and buy one) Occasional crusades against anyone in particular, hate the Church of Ludd.
For the rest of the mods, a warning: I am a terrible starsector pilot, and ymmv depending on if you are better or worse at fighting spaceships than me. Most of theses ships I haven't piloted before, because I get distracted outfitting my favorite ones, like the Nevermore. Some descriptions borrowed from the Starsector+ post.
Blackrock Drive Yards: "Dark green fast and furious ships that favor human pilots, plus a staggering variety of weapons." This is the faction with the Nevermore cruiser in it. Also has the likes of the Imaginos, a ship that would fit in with Exigency if it wasn't bright green and built by Blackrock, the Scarab, a solid but slower than usual Blackrock escort ship, and the Karkinos, a
teleporting capital ship. Afaik the teleporter is the same as the one on the Imaginos frigate, but scaled up accordingly.
Interstellar Imperium: "Orange armored ships packing lots of satisfying, chunky weapons. Favors large fleets and deliberate strategies." I haven't played much of them, but they're alright so far. The description fits.
Exigency Incorporated: "Blue ships with organic hulls, crazy systems, and lots of missiles. Lots, and lots of missiles." You want extra ship systems in your craft? Repulsors instead of normal shields? Masses of micro-missiles, some of which regenerate in combat for even more missile? A splinter faction that builds ships out of stolen Exi parts and asteroids? Blue ships? Exigency has all of that. Very fun to use if you can use them right. (I mostly fail at the latter, but they're still interesting)
Shadowyards (aka Shadowyards Reconstruction Authority): "Green and cyan ships with many varieties of energy weapons. Notably well-balanced." Generally good ships that I can at least try to use without badly failing in the first fight. Rather distinct color scheme.
Mayorate: "Brown ships with lots of big spinal mounts and cool designs. Contains nukes." My second favorite faction of ships after Blackrock. The Lilith frigate is a glass cannon, but comes with a builtin, scaled down version of the weapon the Onslaught uses. The bigger ships are generally interesting as well. AI has a history of not knowing how to evade the aoe of the nukesplosion, use with caution of you have one. One of the rare factions that are not hostile to pirates, they have other enemies to make up for it.
Citadel: "Light blue and gray ships with copious levels of Ordnance Points. An alternative interpretation of 'midline' ships." Expensive ships, but pretty good in general as far as I've tried them so far.
Junk Pirates/A.S.P/P.A.C.K.: Honestly I don't have anything to say about the latter two, I hadn't played with them that often. Junk Pirates have interesting but very messy (intentionally) designs, and are an interesting addition to the pirates of the sector. But now they're in one big triple pack, so have the SS+ description. "Multicolored ships of many tech levels, designs, strengths, and weaknesses. One of the oldest Starsector mods."
Neutrino Corp: Powerful ships. Strong but almost non-existent shield arcs. Lots of energy weaponry and photon torpedoes. I like them.
