Stud gets first pick, unless your agreement says otherwise. You can pay for stud services without the "first pick" contingency. But I hope that you're an experienced breeder and doing it for breed improvement, because backyard breeding is very unsafe for the animals and we don't need more puppies just for the sake of puppies.
If you pay stud fee, no one get first pick. If you get the service free, you could give first pick to stud owner as a fee. However, the owner of the female always owns the pups. It's best to have a written contract beforehand.
Do you have training to breed? Because it is very dangerous if you don't. Botha dogs must be at least 1yr 6mo. Also fixing dogs lets them live longer! And you don't have to deal with the heartbreak of giving up pups -vet