I've used other studs (had my own but never used him with anyone other them my own cats).
Basically, you want to be sure the other person has a record of all shots (and when they were), been tested for any genetic diseases (per the breed).
Would have to see the pedigree of the female and hopefully that female will have been shown to champion or better. Excpetion would be to a female you KNOW has produced top quality cats even if not shown herself. (e.g. Charlie's mom never was shown but has produced more then 5 grand champions
Agreed on the price of stud service and what you guarentee. Most breeders will guarentee at least one live birth - if not, the female can be rebred at next cycle for no additional costs.
You'd have to arrange transportation of the female (usually the female's owner will take care of all transporation to and from the stud). Agree on how long the female will be kept for breeding and where she will be kept.