[IMPORTANT: A lot of the mods here use stuff from the two Library mods: LazyLib and GraphicsLib. Since it doesn't hurt current games and you're planning on trying some mods I'd get 'em and activate them right now, just to be safe.]
For a new player? There's a few mods to help out on new starts.
There's the Steiner Foundation which gives insurance payments if you're low level, and has a shop where you can buy decent combat ships somewhere. I've never tried it but it's up-to-date so it should work fine:
http://fractalsoftworks.com/forum/index.php?topic=10398.0There's also Dynasector which I basically have active permanently. It does quite a few enhancements, mostly for when you have several faction-adding mods at one time. One of the things it does is change the start system, so you can choose a different start with more, more-powerful ships, starting inventory, and with a good credit surplus to start you off. There's also harder starts you can choose if you're feeling more experienced/adventurous:
http://fractalsoftworks.com/forum/index.php?topic=11001.0There's also a mod called "Better Beginnings", you can find it from the mod index, that adds some diversity to the player creation process, but it's basically nullified by Nexerelin/Dynasector. More on the former later.
If you check the mod index, there's a whole bunch of mods in "Utility" and some in "Miscellany". Utility ones can usually be activated and deactivated without affecting your game so you don't even need to make a new profile. There's a few neat tricks in there, like radar and Simulator and audio/music enhancements, and most of them work with other mods enabled. I'd encourage you to browse them yourself if you have the time, see if anything catches your eye.
Before I get into faction mods & Ship Packs I should mention Nexerelin. In a sentence, Nexerelin allows factions to dynamically create alliances, invade, siege and conquer other planets. It's neat and gives you a purpose in the late-game when you have a large fleet but I've found it more intensive than the other mods, especially when chaining up faction mod upon faction mod. You'll definitely have to allocate more memory to StarSector (up to 6GB iirc; default is 1.5GB, someone else can help me out here I hope?) if you want that with quite a few factions or you'll run into save issues as I learned the hard way.
Also, Nexerelin has a different character creation system that overrides vanilla and Dynasector's.
http://fractalsoftworks.com/forum/index.php?topic=9175.0-------------------------------------------
Now that I have those out of the way let's get into ship-packs and faction mods. Just a side note: They're pretty much all compatible with each other so you can easily end up with two dozen mods active at one time if you're not feeling particularly picky, like me.
For a new player I'd suggest trying out the more vanilla-ish ship-packs first, but I'd definitely consider adding some faction mods once you're comfortable with it.
I'll get into the vanilla-esque ship-packs first that I recommend first then:
Hegemony Expeditionary Auxiliary Fleet
http://fractalsoftworks.com/forum/index.php?topic=11948.0Basically a mini-mod, it adds Hegemony Auxiliary variants to the Venture, Mule, and Shepherd. Blends perfectly into vanilla and I think I was actually able to add this in the middle of a game with no issues. (No promises though: Please don't sue me if trying that crashes your computer). It's a nice bit of extra fluff and the upgraded Venture can be especially dangerous for its cost with the right builds, compared to the civillian version.
Ship&Weapons Pack
http://fractalsoftworks.com/forum/index.php?topic=11018.0Does exactly what it says on the tin:Adds a bunch of ships & weapons that seamlessly blend into Vanilla Starsector. Excellent for variety while keeping that vanilla feel. The only tiny thing is I those cheap, low-tech weak Mini-Blaster weapons seem to be rarer than Plasma Cannons because I just cannot find them to save my life! But that's a personal issue.
Arsenal Expansion
http://fractalsoftworks.com/forum/index.php?topic=11536.0Similar to the S&W P, it basically adds new ships and new weapons. It doesn't have quite as many ships IIRC, but it also blends into vanilla. Again, a good choice for an expansion that keeps your vanilla feel.
Disassemble Reassemble
http://fractalsoftworks.com/forum/index.php?topic=12360.0This one's a kitbashed one, so basically the author took a bunch of parts from other ships and sprites and combined them into new vessels. You probably wouldn't realize that unless you're told it, as quite a few of these are very good-looking and unique-looking vessels. As with the others on this list, adds new ships, new weapons, and keeps your vanilla-feel intact. Of particular mention IMO is the Lysander DD Leader, a very good mid-tech ship with an Operations Center which makes it a great flagship, and the mod's good number of Luddic Path variants (don't stand still near Piranha LPs, and don't stand in front of a Retribution LP with anything smaller than an Onslaught.
Underworld
http://fractalsoftworks.com/forum/index.php?topic=11002.0Okay, so this one is technically not a pure Ship/Weapon pack like the rest, as it adds a Pirate system and a new faction, the Starlight Cabal, who are basically purple pirates who were never told "no" by their parents. But it's a perfectly vanilla feel so I'm including it here anyways. Underworld is basically a pirate-themed ship-pack, so a lot of scrappy things to blow up, but some upper-level pirate stuff is also there that can blow you away if you're not careful. If you like some of the higher-tech vanilla ships (like the Medusa or Aurora), there's probably a Cabal version that'll improve its every facet, except maintenance costs (the purple makes them powerful).
The only real downside I'd say is the lack of a Cabal Paragon, but then again that may be for the better.
Finally, it adds a pure pirate system called Styx. There's a guy there around Arigato named Dickerson you should definitely kill.
Finally, there's a whole bunch of Faction Mods. These mods add extra systems, markets, ships and weapons with their own specific theme. I'm not going to list all of them so I'll just do the ones that are Dynasector Compatible since I've personally messed with most of those. All of these are listed in the Dynasector Link given earlier so I won't link 'em here, just give them a brief description of what the factions are, their strengths, anything else notable, etc, to give you a general idea of them so you can pick what you like.
(Disclaimer: I generally prefer stuff that has a more "vanilla friendly" flavor which undoubtedly influenced my choice and opinion of mods, take my opinion with some salt.)
Blackrock Drive Yards
Haven't played with it yet. Ships look good. Idk why I haven't tried it yet, probably because I can't seem to find any fluff or lore on the page (I prefer to understand their place in the universe before adding them, so to speak).
Diable Avionics
Haven't played with this yet either. Ships look fine, and apparently some of them transform into 'Mecha and stuff, which is definitely different. If you want to see transforming starships, that's your mod.
Exigency
Haven't played with it yet either. Probably the most exotic of the Dynasector-Compatible factions, apparently this mod's faction doesn't even use shields and have some sort of exotic alternative. It's likely a good bet if you're feeling like trying something out of left field, but not compatible with 0.8a (current SS version) yet.
I swear I've played some of these, we're getting to 'em.
Interstellar Imperium
Space Rome. They consider themselves to be the inheritors of the Domain of Man, and thus considers the Hegemony to be their archrivals. One of their systems is beautiful, full of super-terrain and the Imperium's capital, you can find some good stuff exploring that system. The Imperium has the Matriarch, my personal favorite Carrier in all of Starsector and its mods (yes, more than an Astral). Mostly mid-tech level ships, and quite a few good and unique weapons that benefits the game IMO.
Junk Pirates/PACK/ASP Syndicate
This is a pack of minor factions. The ASP Syndicate is a tiny faction with a few combat & carrier freighters, PACK has more ships including a light Battleship & a variant of it. I can't give a good opinion on the Junk Pirates because their ships are so hideously asymmetrical I intentionally give wide berth to their fleets, which considering I often conquer Chicomoztoc with Nexerelin enabled means their sheer ugliness is effectively a much more effective defense against me than any number of Onslaughts. Is that irony? (Not knocking the mod though, don't mind their presence and have had the mod on for a while, I just prefer them present away from my beautiful, very symmetric fleet.)
Knights Templar
Haven't tried it. Basically a "boss" faction with very powerful ships and weapons. Get it if you want a challenge.
Outer Rim Alliance
Speaking of symmetry, the ORA is probably the most beautifully symmetric ships you've ever seen. They're probably the closest to the universe's Good Guys that you'll ever get to. They're broadside ships though, so it's not for everyone. Does have my 2nd most favorite carrier in the game, the Discernment (?) with 8 fighter slots, but its special ability is a bit of a letdown for a Capital. The ORA's extra systems do include some hidden goodies if you know where to look, including a hidden Pirate market. Oddly enough, I find their ships work best when installing Shadowyard's weapons on them, especially CEPCs.
Scy Nation
Haven't tried it yet, but since reading (skimming) the fluff I've been meaning to. The bad TL;DR version: A Domain Science Colony has a tenuous existence and no friends after the Collapse, a Luddic Radical genocides a whole bunch of them, and they end up surviving and establishing their own nation under a benevolent dictatorship.
Shadowyards Reconstruction Authority
Good high-tech ships, including several new Phase ships. The Scylla is a dangerous Phase Cruiser, and the Charybdis is a versatile carrier cruiser. Their energy weapons, especially various CEPCs, are very solid weapons that go extremely well on anything if you can afford the OP cost. Also introduces some pirate versions and Persean League versions of Shadowyard vessels. The portrait art style differs from the vanilla-style but that's not very important.
Tiandong Heavy Industries
Haven't played it yet as it's not compatible for .8a, author's waiting for .9 for next release IIRC. Includes mostly heavily modified vanilla variants with some odd renamings for them, and some good looking weapons, especially that Triple Mauler battery which makes me want to build an Iowa BB in Space. Overall looks quite vanilla-friendly.
Tyrador Safeguard Coalition
High-tech ships that generally look a bit more rugged than other typical high-tech ships like Shadowyards and Tri-Tachyon. Actually, the mod includes some TT skins of Coalition ships, as well as Coalition-variants of vanilla ships. Features a nice-looking and unique forge-world with an industrial ring around it. Includes an interesting mission with a really large Coalition "Forgeship" & a battlestation. The Lance-class Cruiser is a fantastically versatile vessel that you can outfit for just about anything. Doesn't seem to have as much stuff to find when exploring the system as the ORA and Imperium's systems, though I could just be bad at finding things.