Ordinarily, I'd expect the shop to purchase the parts. Then, they'll put a mark up on it and add it to your final bill.
However, if you've found a guy who is self-employed, running a small shop and is willing to work with you (and only charging enough to get by, e.g., $45/hour), he may want you to pay for parts upfront. If that's the case, ask if he has some customers you can talk to (references). If he has good reviews *and* his record is clear with your local better business bureau, then I'd say it would be fair to pay him for the parts upfront because he may be operating on a shoestring and passing the savings on to his customers.
That said, if he doesn't have references (if he acts offended by the question - red flag!), or if there is anything questionable on his record with the BBB (or your local state's attorney's office), don't do it. Keep shopping - you may never get those parts installed and lose your cash as well.
