Should I use a contract?

I used to avoid using a contract, but because it provides "peace of mind" for the client, I have developed one and use it when there is sufficient time between the contact and the performance. 

The principle purposes of a contract might be one of two things.  The first is a formalism for communication and the second is to provide for protection against loss in either a real or perceived sense.

The essentials of a contract are:

Who: Contact information including the name, address phone number(s) and email of the parties involved (musician and employer).
What, Where, When: A description of the event including the type, date, start time, end time, specific tune, tuning and rehearsal expectations if any.
How (much): Payment including any deposit.

Legalities: This is left to your taste, but should include provisions for cancellation by either party.