The type of microphones (often shortened to mics) that you use in the studio will differ from those used in a performance. Studio vocal microphones will be the large diaphragm condenser type such as the Rode or Samson ranges and for live work you would use a dynamic mic.
For live vocals, the industry standard is usually the Shure SM58. You will also find that you may need to mic up an acoustic drumkit which will need different ones for the bass drum and overheads for the snares and cymbals.
There is a wide choice of microphones available and prices vary from a few pounds to those costing hundreds.