Hmm.. really I think you'll just have to rely on finding a good company. I'm not aware of any that are set up to have, say, a list of profiles for all their writers listing qualifications, etc., for you to pick from.
As far as I know, the model most all of the sites use is that you submit your request, interested writers indicate that they want the assignment, and then some higher-up person chooses one of them. I've heard that some sites have a sort of 'Advanced Writer' designation that lets some writers automatically claim assignments.
I've only worked for one company so far. It has an actual office and a few of the higher-up people working onsite decide which interested writer gets an assignment. I'm pretty sure academic qualifications factor into their decision to some extent, though I've never requested something way outside of my expertise (I stick to the humanities, so I don't request e.g. finance assignments) so I can't say for certain. They do email/call me to make sure I have access to any specific books/documents required as sources so they can get the client to scan and send if not, so it seems like they're careful with it. They also factor in a writer's track record for quality - someone looks over and manually approves everything before it goes to the client. That's probably the best model you can hope for until you're a repeat client and want to request whoever did your last paper.
So best of luck! My advice would be to call (on the phone) any companies you're considering and ask about how they will ensure you get a qualified writer. If you can't get in touch or they can't give a satisfying answer, keep looking.