Basic round wire is the most common to use for most wire wrapping.
Half-round has one domed side (half a circle) and one flat side. The flat side is sometimes useful in short pieces at the beginning of a project.
Square wire can be twisted for a very pretty effect, but isn't often used.
Your next question is likely to be "What is the difference between half-hard and dead-soft wire?" Dead-soft wire is very soft and easy to work with, but does not hold its shape well. Half-hard wire has been tempered so it is stronger (and slightly more brittle). It is harder to bend, and holds its shape better. You'll almost always use half-hard wire when making jewelry.
Here is a quick link to all of our wire and sheet
We carry a nice variety of books about wire-wrapping and wire jewelry
. All Wired Up: Wire Techniques for the Beadworker and Jewelry Maker
, by Mark Lareau is a good choice, but depending on your plans and style, there are many other good books available too!