I prefer a mic over a pick-up, though I do have pick-ups in all of my guitars, since I do realise that there are situations where they are needed. The option of playing the mic; moving close for solos and back for rhythm, is not available with the pick-up. I have been told that I should get a volume pedal for this.
When I supply my own mic, I use a Beta 57 for an instrument mic and a SM58 for vocals.
Some venues supply the sound system and the mics are usually an SM57 and SM58.