Well, I'm Sicilian so I should know everything about Paving

Honestly, I'm in the computer business but know of MANY people in the paving business. Even worked there for 1.5 months many years back when I was thinking about quitting school. Good thing I didn't!!
Few things I would look at
1] Warranty - they should be able to give you some type of warranty, 1 year is pretty standard
2] How 'reputable' is the company? How many years in business? Any other work? Any references? Paving is the type of job people do for 1-3 years then claim bankruptcy and open under a new name. Paving is 75% a cash money business
3] Ask if you can pay cash and avoid the taxes (should be easy for a paver)
4] Asphalt quality is important but hard to measure. Staying with a reputable company is a start. Obviously needs to be applied hot. You should not see many rocks in it and when they finish it with the rollers it should be smooth!
5] Thickness of asphalt if not THAT important. it should be about 2-3 inches but 2 inches would be more than fine. The MOST important thing to worry about is preparation. They need to use crush stone as the base and need big heavy equipment like rollers and compact machines. If they don't have a roller, it wont come out very good. I would much rather have more base (crush stone) than Asphalt. More Asphalt will not make it stronger, it depends totally on the preparation.
6] Don't make them do a re-surface. Re-surface is basically putting more asphalt on your existing and then compacting it. This is the cheap way out and will result in you needing to do the driveway again very soon.
7] I would prefer to prepare the driveway one day and a 1-3 days later have them come back and lay the asphalt. This will give the driveway some time to settle.
Hope this helps.