Certainly. The only reason you'd really want to upgrade from that mixer is if you wanted to use several microphones at once. Shure SM58 is an awesome microphone, it is my daily microphone at the moment. A couple other awesome microphones to look into before purchasing would be:
New and updated version of the SM58. It uses the more modern Neodymium magnet, which makes it slightly more sensitive. So you can expect its output to be slightly louder. It also uses a super-cardioid, unlike the SM58 which uses a standard cardioid pattern.
Extremely comparable to the Beta 58. I mostly hear people prefer it with higher pitched voices, and that it is a microphone to avoid for really low voices.