Microphones & Stands
Cost-wise they are a relatively cheap portion of the overall cost of a live system but it isn't worth skimping here.
Vocal Mics
The most common type, often called '58s' in relation to their 58mm diameter pickup or sometimes just Shure 58s after the popular brand. They're extremely versatile and robust (if you don't drop them on the floor). They have a 'cardiod' pattern which is like a balloon, ideal distance being 0 to 6 inches from the mic.
The simple rule is that you always need one more than you have because they're so useful. If you normally use 3 then you'll want 4 for that occasion when another singer turns up or you need to mic an amp. As they're quite hardy bits of kit get an extra if you can afford it.
Condenser Mics
There are many varieties of condenser mic, which range from the reasonable (paired for under £100 with a stand) to the studio-level ridiculous (£1,500+).
Excepting specialist mics like for saxaphones a basic condenser set makes it much easier to capture sound from things like violins, drums and other instruments. The different sound pattern (more like a tube than a balloon) picks up the music in a more directional fashion.
However the musician needs to be aware they can't be used for vocals, the number of times we've seen musicians singing into a sensitive instrument mic!
