Hi, Phyllis- You will want to use hard or half-hard wire for your
wrap. Half-round wire is normally used for the binding wires on
wraps, but is not necessary. Round or square wire, depending on your
design, is probably what you want to go with.
I strongly recommend that you either acquire a book or two on wire
wrap, or find someone willing to give you a lesson before
proceeding. Anyone who says "what could be hard about bending a
bunch of wires" can find out by attempting to wire-wrap! Not that
the skills are difficult to acquire, it's just that there are some
tricks in terms of how to use your pliers to make clean-looking
loops, bends, etc that will make a lot of difference in the
appearance of the finished piece.
By the same token, producing a simple, attractive wire wrap is not
terribly difficult. Get a book, and/or get a lesson, and then have
at it! Good luck!