Well... walking around in the city is a good thing, sepecially when you're waiting to be picked up. So, you can't do anything except walking until they come to take you. And my advice to you is - patience... don't be hasty. You must learn that everything in this game takes time :). Buying a ship is a difficult task but your faction will assign you a ship, which you'll be able to pilot freely.
Since the Combine is not yet complete, most of the real action takes place within factions - in the form of RP, earning salary, and completing tasks for them. If your faction is too unresponsive for you, I would advise trying a different one.
As Revan explained, buying ships is not something that will be an option for you right away, since ships cost a bit of money, so it is best to start earning some salary from your faction before you start trading. They should assign you a ship and provide transportation to it, though, so this should not be a problem.
Since there is no combat yet, buying weapons is not terribly useful or necessary yet, but if you want to do so anyway, there is a small selection available from NPCs inside shop facilities. There should be a shop in every race's starting city.
You should also take a look at "The Guide" (http://www.swcombine.com/guide/ - and linked at the top of every page) to learn a bit more about SWC.