XC (mountain bike) tire for dry hardpack and loose conditions
A good quality bike tire usually has a better size tolerance, a better rubber compound (might make more difference on traction than thread geometry itself), a better seating on the rim, and a better "feel" - the tyre carcass reacts better to bumps and curves, have a good cushioning effect and a good rolling resistance. I'd say there is a perceiveably relationship between price and quality, or at least the vast majority of low-price tires are not very good compared to medium- to high-priced ones;
For the described conditions, I'd say 2.0 would be best, some might prefer 1.95, some up to 2.2. More than this is possible, but probably not necessary;
Cannot tell about price range, depends on country;
Tires are funny in a way that the best tires (so as the best suspensions) do their work quietly. If you notice that you just GO, enjoying the trail and never ever having to think about the tire, traction, cornering control, pinch flats, etc., then the tire is good, it's doing its magic. Not-so-good tyres constantly remind you they're there, and you end up thinking: "this f***ing tire sucks!";
Tire models/brands are a very personal matter, but I had good tires - ones that did their magic - from (not in any order) Bontrager, Specialized, Maxxis, Ritchey, WTB, Panaracer, Tioga.