If you have no contract you have basically no recourse for anything as a CONTRACTOR. For instance they decide they want to pay you monthly....you don't have a contract that says you were to be paid every 2 weeks and it'll be an uphill battle to try to change this.
You have no employee protections as a contractor so the only thing that lays out your business transaction with the party you are contracting out to is ahem the CONTRACT.
So yes bud you need a contract.