"How often should I save?"
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That's up to you. It's usually a good idea to save just before entering an unexplored JP (in case something goes wrong) and just after (so that you don't "lose" the system you just generated if you need to do a restore)....
So if you don't like the new system that is generated it sounds like you could go back to the save and keep transiting the JP until you do? I would view that as "cheating" but curious minds want to know.
*moved to The Academy from an FAQ thread*
Yep. Aurora doesn't try to prevent you from cheating at solitaire.
John