When I use stripes to bind a quilt, I cut them on the bias. They look really nice this way, and you don't have to worry about being a little "off". I *do* heavily starch the fabric before cutting the bias strips. The starch keeps the bias from distorting during handling.
Oops! Sorry, I missed the part about self-binding. I simply refuse to do quilts with self-binding. They never turn out well for me!