Starbound was always going to be a game that players would want to re-build in their own image. A procedurally generated sandbox means systems. Lots and lots of systems. It means the community can change whatever they want, and the players have responded at a phenomenal rate of moddery. I've done ridiculous things to my game that I'd never recommend you do. I've added a Dubstep gun and a Vuvuzela*. But there are broader changes I'd happily recommend: tweaks to ship shapes, planet generation, better farming. There's as much to explore in the modding scene as there is on Alpha Diadem 028 III C, and I've beamed down to have a look.
Before you do anything, install this Starbound Mod Manager. It acts like teacher on a school outing to ensure the mods know what they're doing, where they need to be, and how to get along. That's really important when dealing with potential incompatibility between mods. It'll do all this while preventing changes to any of the game's core files, which is probably its most invaluable trick.
And because I dared to start with something as utilitarian and emotionally crippled as a mod manager, my next suggestion would be to grab the Creative Mode mod. It features in both Starbound Nexus and the official channel's "top mod" list, and allows you to play a free-form Jazz solo with the game's items. Its purpose is simple: to allow the players to access as much (though not quite all) of the content as and when they need it. It's the toolbox to unlock the actual sandbox, so you have a lot more resources and abilities available, like invincibility and a super-powerful matter manipulator. It could seem like a giant box of cheats, but the flight mode reveals its true purpose is to enable players to construct anything, unbound by the notion of grind and gravity. There's still some smelting and crafting involved, which I like because it fits into the game's theme, but this is perfect if you're looking to make something of the world.
Starbound's beta status is obvious when you play it: you have all those tools to reshape the world, but you can't reshape your ship? All you have is a cramped rectangle that that an estate agent would label as "cosy". I imagine reshaping your ship so it's more shipshape will be coming in an official update, but I can't see it topping Spaceship: Block by Block Building. Your ship can be completely torn apart and rebuilt using any of the game's materials, and it adds the early stages of a complete overhaul of how the ships work: life-support, landing pods, teleporters, etc. There's more to come from this mod, but if you want to see what it's capable of, just click the main image of the article.
But it doesn't work on servers, which makes me sad. Who wants to spend all that time retooling a ship - retooling it into a glorious space phallus - if people can't admire it? That is the point of self-expression, isn't it? If you're happy to work with just the base materials, and can do without the extras, Fully Customisable Ship will let you build a ship other players can admire in vanilla multiplayer.
But where could you take that ship? The universe Starbound creates is one of gaming's most impressive feats: star systems with explorable planets and moons, lovely backdrops of desert moons, forest planets, and arid, evocative landscapes. Variety Is The Spice of the Universe adds to that in some wonderful ways, turning the weird and exotic up a notch. There are Frostfire planets with sub-zero surface temperatures and pools of lava, Tarballs are dirty rocks of slime and bones (and tar), and many more. On top of those are biomes as well: metallic moons, or huge mountains, or spooky forests. And there are a few more modifiers, like acid eating away at the savannah. I can't say I was ever bored exploring in Starbound, but with this installed I'm almost sure I'll never be bored again.
To make sure of that, I uninstalled it. Why? Because I found the sadly incompatible Wastelands Planets, and I just had to have it. Despite everything Starbound is capable of, it doesn't do desolation very well. That's clearly a stylistic choice by the developers, and though there are abandoned places, they don't feel old. Wastelands Planets are post-industrial places: cracked, grey, lost. It's the backdrops that really sell it, with tilted, post-apocalyptic landscapes creating a lovely mood for the rubble and the ash storms.
It seems like the perfect place to take on Per Aspera Ad Aspera, an in progress mod that has some evil plans. I'm suggesting you keep an eye on this rather than installing it now, because the plan is to basically overhaul the complexity of the game, turning it into a ridiculous, complicated adventure where material properties extends to things like thermal conductivity, organic protection, temperature stabilisation. Just look at the list and tell me you don't want to be dealing with nuclear fission and colonial warfare.
Hmm, things are getting kind of bleak. To counter-act the destruction and darkness there's Persistent Farmables. It's one of those mods that would be right at home if it was added to the vanilla game, making crops grow when you're off-planet and on adventures. You can even have them sprout when you're not even playing the game, which makes complete sense to me. A living breathing universe should tick along when you're not around. I love the idea of coming back to something that you've planted as proof that the world kept on going when you were asleep.
I have a similar love for Your Starbound Crew, which adds a crew to your ship. Aside from making your ship feel less like an escape pod and more like a wagon on the final frontier, the crew act as nodes for a lot of the game's content, enabling you to unlock supply merchants who'll hang around your deck. This means you're always able to find an item without needing to craft or hunt down what's needed through trial-and-error. As long as you can afford it, you'll be able to access food, meds, tools, weapons, and even the lore that underpins the universe.
*Though I drew a line at the Aryan Race mod :(