The best thing to do would be to ask someone that has already done what you’re about to do.

I don’t even live in the US so don’t take my word for it but here’s what I know, assuming you’re just there to record:
- The contract is provided by the employer. You sign it, they pay the musicians union, you go to the union office and get your check(s). Here are some contracts used on some very famous record dates: http://wreckingcrewfilm.com/contracts.html
- Unless you’re the writer and need an advance to cover some of the expenses (booking studio, hiring musicians, etc …) I don’t think you can ask for an advance.
- If you’re a member of the musicians union and this isn’t a union gig, be careful because if they find out about it they’ll fine you.
- If you have to do the contract yourself be very careful what you put in it and how you word it. There can’t be any ambiguities. Three tracks is a very, very loose term. It can take you an hour or it can take you a month to get the job done. That’s why it’s better to be part of the union. There are hourly rates that vary depending on the type of date and how in demand you are (if you’re an A-list player you might get double scale). They also hire you for minimum of three hours. In other words, if you get the job done in 30 minutes you still get paid for 3 hours.
- If you’re just starting out don’t nickel and dime yourself in terms of money. Focus on doing a great job and that’ll ensure you’ll get called back.