I believe past history is a great predictor of future work, so I would ask
1) Have you worked with anyone in our industry or similar project?
2) Ask for their complete portfolio
3) Ask them how many full time vs. contractors
4) Ask them who on the team (or individual) did the work you like and if they would be available for your project?
5) Ask them to asses your idea and come back with 3 highlevel ideas via email or powerpoint.
If you're going to be spending $10K+ then I think it's fair to ask them to do a bit of work to demonstrate how they would approach your project.
My rule in life "I can't work with you, till I work with you".