I am a wire wrapper, I teach traditional wire wrapping locally and sell tutorials. I would suggest that you take a beginner class locally so you can start with good technique & the basics - straightening wire, bundling square wires, about the right tools, wire hardness, gauges and types.
Depending on what I'm doing I used either dead soft or half hard wire, I prefer sterling silver wire, usually square & half round, ranging from 24 or 26 gauge in viking knit to 10 gauge for a neckwire omega.