No, you cannot pick another starting location.
No big deal, though. Just means that it'll take some factions a bit longer to pick you up.
You could buy a ship, but starting prices are around 100,000 credits for a small fighter.
You can join a faction, look through the list of factions ( http://www.swcombine.com/community/factions.php ), find one that appeals to you.
Click on the faction button in the right side menu for the join faction button.