I can't figure out how to get a speeder in the first place. I have a level 20 character, but still don't see anywhere to learn or buy one. And I see people using them all over, so I must be missing something.
Actually what you're missing is 5 levels. You get the speeder ability at level 25, not level 20.
The people you see using a speeder at level 10-24 spent 40k on a Legacy Unlock (which requires Legacy level 10 irc).