My goals were different from yours; I wanted to live with other people with some sense of community. And I didn't mind pets. Found two lovely ladies and a dog in a little old house, head students like me. We were never bffs, but were a great match as roommates. Shared pantry staples (eggs, sugar, flour), never needed a formal system for paper & cleaning products (just took turns), traded off some chores and favors (dishes vs trash, watching her dog vs homemade pie), planted a veg garden together, had cookouts.
I think the biggest conflicts among roomies tend to be cleaning, noise, sharing, and visitors, so those are important to talk about/screen for. A slob and a neat freak will have a very hard time cohabiting. If you have a long distance SO, living with someone opposed to overnight guests would work badly. Etc.
[ ETA: Realized after posting ability to pay rent is very important, too. Definitely looking for steady employment and a healthy attitude toward money, ie prioritizing rent.]
Screened my current roommate by dating him 3 years. Sometimes wish he'd clean more, but overall it's pretty great ;)