For your first purchase you'll probably want a speeder or swoop bike (take note, not a landspeeder, which - I believe - is slower). No matter what planet you start on, there should be some on the bazzar for that planet if not that particular city you're in (only makes a difference in how inconvenient it'll be to pick up). There'll be dozens for the minimum, ~4000 (not sure what sets this price, maybe vendor components or bazaar fees, I don't remember) so you'll need to run some deliveries.
Find a mission terminal, switch to the delivery tab, and look for deliveries that reward about 1000+. Pick up two whose end destination is going to be at about the same distance in the same direction (e.g. 8000m NW). Get your stuff from the NPCs and check the planetary map for what city you're heading to. Head to a shuttleport and buy a ticket to take you there. Deliver the goods, repeat.
If you're doing combat, you'll probably want to buy a better starter weapon than what you've got. Check your skills window to see what weapons you're certified in, then look in the bazaar for a crafted weapon of those types; it'll probably run another couple thousand. Or roll Brawler and just Unarmed Combat things to death; TKA and TKA-based hybrids are apparently as strong as they were back in the day. Honestly, combat in SWG is kind of... not weird, but I'd guess unpolished. You'll notice what I mean when you start shooting things. In any case, I've only ever played pistolleer (even back in the day, hopefully it's not as broken as it was back then) so I can't offer a whole lot beyond that. Someone else with more knowledge than me would be better to direct you in that way.
Also, you'll probably want to go to Options - Controls - Keymap button - Load a Standard Keymap: MMORPG (EQ style). This is the more or less now-standard WASD controls, although there will still be some strange differences (m brings up the radar map overlay, where v is the full colour window planetary map that may look more familiar), but of course feel free to rebind things as you see fit. You might also want to get used to using ~ (tilde key) to "activate" NPCs and objects, opening the radial menu so you can interact with them (which you can also further shorthand via number keys).