Definitely go with a used bike. Not only for the reasons that VoodooLogic mentions, but also because you’re almost assured of finding a better deal. There’s always some dude getting married or having a baby or in some other way being forced to rid himself of that one last vestige of his youth. That’s where you step in to get a nice, cheap bike.
But to answer your question—what kind of bike are you interested in? Sport bike? Cruiser? Touring? What kind of riding are you going to do? Long-distance, or in-town commuting? Do you want to go fast, or save on gas (in which case your best bet would be to stick with the Vespa)?
Most importantly, you’ve got to be honest with yourself about how much bike you can handle. Your life truly depends on how honestly you answer that question. Motorcycles are inherently dangerous. Getting on one that is too big/heavy/fast will kill you.