The Mustang if you want to have more of a fighter and the Aurora if you want to do a little more of everything. The Aurora's kind of like a space Civic, it has less guns than the Mustang but you can carry a missile rack (for an additional cost, anyway) - plus you can even sleep in the rear, and it has cargo room. The Mustang is more agile and can carry more guns but no missiles.
Edit - As Zalusithix mentioned, I guess it depends on if you want to throw more money in, but between the two cheapest starter ships those are my thoughts. Plus you can buy any ship in the game with in-game currency once you start playing, so you don't NEED to spend any more than the starter package, but you COULD if you wanted to. Personally if I were to choose between the two I might side a little more with the Aurora unless combat really is your thing.
More Edit - Even if you choose the cheapest option, if you join an organization (like our fine GAF Org), you'll have plenty of opportunities to do other things like being crew for trade runs or being part of a larger ship's crew - we have 3 Idrises and a billion Starfarers and Carracks in the GAF org and volunteers for crew would always be welcome. You'll never be stuck with just Aurora or Mustang duty if you play your cards right.