When I first played a few years ago (PC) I spent quite a few of the initial hours checking out the marketplace prices and shifting a few items between planets for a little bit of profit. If you can combine this with a couple of the easier shipping / transport missions then all the better.
This got me used to controlling the ship and moving from planet to planet without getting me into too much trouble (although I still got into some scrapes with pirates) - and because there is so much freedom, and so very little hand holding, the game really is at it's absolute best when you just mooch about doing a few bits and pieces and learning the ropes.
There's plenty of time to turn yourself into a hard core bounty hunter later on