Asphalt is fine but will eventually crack and it does need periodic resealing. Also any jack stands, jacks, etc. is a no-no unless you set them on something to distribute the weight. Concrete is best. But if you get concrete, specify rebar in it. And specify that any control joint be sawed across an area of full rebar. That way when the joints crack, if it goes to settle, the rebar will hold the two areas at the same height. Wire mesh can stretch and allow for uneven joints if settling occurs. And the fibermesh concrete will not prevent any of the above from happening. It is good stuff but not a cure all for problems. Also whatever type of drive you put in, make sure the base is firm and compacted. The best bet if you know that you are going to be putting a new drive in and you don't yet have a base, get a good gravel / ballast base and drive / park on it for a few months before the driveway is ever put down. I have seen new drives cut in, gravel dumped and smoothed out, concrete poured, only to be cracking out a year later due to settling.
Kevin