Pat:
I spend the non-hunting season cycling, so I have a litle experience. First of all, as a rule-of-thumb, I recommend that people spend at least $1000 for an adult bike (i.e., not for a child), otherwise they will be disappointed with the quality of components, wheels, and overall quality of the bike. With a budget of $500, you are looking for a used bike, or last year's model that has been marked down (between now and let's say March may be a good time to find a good buy on last year's model). The brands that you mention are all top brands, so you're OK there.
I am not sure what features you will need for a "hunting bike"-depends on the terrian you hunt on and what you plan to carry. A couple of ideas though:
1. Think about getting suspension (shocks) on the front but not the rear (a "hard tail" Mt bike). A hard tail will be much easier for mounting racks, pulling a trailer, etc.
2. Get disc brakes - they perfom much better when things get wet and muddy.
3. Get a bike with rear rack mounts, if possible, although this is not all that important because most good racks come with mounting hardware that will work with any bike.
4. Bikes with two wheel sizes available, 26" and 29". I have bikes with both wheel sizes and I would recommend the 29" bike, which rolls over terrain much more easily and faster. The downside is that a 29" bike may not be quite as nimble on steep, rocky terrain. Try to test ride both sizes if possible.
My experience helping friends buying a bike is this-if your are in doubt between two bikes with different a quality level and price, then buy the more expensive, higher quality bike. Otherwise you may be disappointed and end up getting a second, better bike later.