One or both on the lease?

[Denise Holder]

Hello, I am about to rent out my first property! I have a couple questions, 

How do I check the prospective tenants credit scores?

My best prospective tenants so far are an unmarried couple.  Should I put the lease under one of their names (the man makes most of the money and says he has great credit) Or both, I don't know yet what the woman's creditworthiness is.  But if she meets my minimum requirements, should I put them both on the lease? If they break up, I might have a better chance of getting my money from him. If she takes off, but is responsible for half the rent, I might have a hard time getting it from her.

Thank you!