For about 99% of your mystery shop payments you will need only three things.
1) PayPal address - Go to PayPal.com to set it up,
2) A bank account - you provide the routing number of your bank and account number of your account to the MSP, and
3) A mailbox - for paper checks.
Nearly all companies provide payments in one or more of these ways. Some offer only one option. Some allow you to choose from more than one option.
ACE is the only company that does things differently. It uses PayQuicker as their only payment method. Last I heard they were in the process of transitioning to another method.
As for fees, most companies deliver the payment without any fees. Expert Solutions (Stericycle) and a small number of MSPs deduct 3% from PayPal payments. But Expert Solutions also allows you to choose direct payment to a bank account that is done without a fee.
When you go to a company website to sign up, they will often ask for, and many times require payment information to start shopping. For those that mail paper checks it is easy to supply a mailing address. For PayPal payments it is just as easy to supply a PayPal email address after you set it up. Setting up a PayPal account is quickly done as well. Deposits to a bank account can be more time consuming in that some companies want a form faxed to them. Either way, this is a necessary part of setting up your business.
Hope that helps make it easy for you.
Have fun!
Happily shopping Rhode Island and nearby Massachusetts and Connecticut