renting to students - who to sign on leaser

[Roy Mitle]

I have a 4 bedroom townhouse that 4 students want to rent together. They don't have income but their parents have sufficient income. For the application form who do I get background check on? Ideally I want to check their criminal background/rental history and their parents credit check/employment check. Also do I need every parent's credit check. All of them have well to-do parents so it should be easy for just 1 set of parents to pay rent for all of them. 

Also for signing on the lease do I have them sign it, their parents sign it or all of them together.