Bobert gave you very good advice, Chico, when he said to start by performing "stuff you could do in your sleep." Don't try to display your most impressive new stuff in the beginning. If you're nervous about the piece as well as about performing, you're bound to flub it. Start with the tried and true.

Maybe before you do any of these performing things, you could practice performing for a few friends. (This is less risky for a musician than, say, a brain surgeon.) I am assuming you haven't done this because you say you haven't performed for ANYONE.

So order some pizza, and invite a couple of friends over, with the agreed-on agenda of playing for them for half an hour to an hour. Get feedback if you have the nerve, otherwise just use it as a learning experience. Once you've performed for a small group of people, you will have a few "seasoned" songs in the sense that you know you have performed these in public and nobody threw tomatoes. For me that has always been a confidence builder.