Microphone for recording vocals/singing by: Microphone Guide
It all depends on how much you're willing to spend. So without knowing your budget it's hard to say. The higher your budget the better your chances of getting a high quality microphone.
There are two main types of microphones for recording. They are dynamic and condenser microphones.
But if you're on a budget, when it comes to recording, the number one suggestion for dynamic microphones is the Shure SM57.
Condenser microphones like the AKG C414B (which I personally use for recording at home) cost a lot more. A quality budget condenser model great for recording singing (vocals) is the RODE NT1.