Inexperienced landlord needing advice about screening applicants

[Amy Martin]

I'm in the process of renting out our first rental property. I started showing the home yesterday for the first time- did 5 showings and received 1 application. I am fairly new to real estate investing and would like advice from more experienced landlords: 

Income: The application was from an engaged couple in their late 30s. The man works in a fairly popular restaurant as a cook and makes $2000/mo. The girlfriend works as a waitress in a different restaurant and makes $2600/mo (80% of which are tips). 

Rental History: The girlfriend seems to be moving every year...for the past 3 years, she has stayed at 3 different rental homes. Her reasons for moving are "moving closer to work; moving in with fiancé; needing a bigger space". The boyfriend moved about every 2 years. 

My questions are: 

1. Is it a good idea to rent to an unmarried couple both of whom work in the restaurant industry? To me restaurant jobs are not stable. Plus, if they break up during the lease term and one leaves the house, the other one wouldn't be able to pay rent on his/her own. 

2. How do you guys analyze an applicant's rental history? Is it a bad indication if an applicant constantly moves from one rental home to another, every single year for the past 3 years? 

Any advice would be greatly appreciated!!