Your plans with that stars-system sounds interesting. But, just wanted to mention, you don't necessarily need other players around, to want to know your best score, because after all, you don't want to have to write it down every time. Plus, there are times when you might want to show your highscore to a buddy, to compare it with his best score, and so on. So, a highscore-list definitely serves a purpose, even if you're playing solo, just wanted to mention that.
That said, the star system you described, sounds pretty good, too, as I already mentioned. Fewer moves, to complete a level, could/should also mean earning more stars, that could also rise the motivation. However, if a list for the score isn't planned, the game should at least display the highest reached score so far, somewhere on the screen and save it to disk, when a player makes a new highscore. Maybe a player wants to know later on, how many stars he already had achieved, after all. So, these are all just suggestions, of course, it’s up to you, how you actually do it.