I don't think your stupid at all. Other than the dangers of combat, if your job entails that it is hard to beat the benefits unless you have a good skill in the civilian world. Especially if your single, you can spend every penny you have and still have insurance, a place to sleep and a place to eat 3 meals a day. And then if you can manage to stay in long enough you can retire with a pension and enough time left in your life to enjoy yourself.
If I was infantry or something like that I might rethink it simply because of the danger involved, more so if you have a family. However for a support type job where you weren't actually getting shot at all the time its not a bad deal. I didn't like all the B.S I had to put up with in the Air Force, but now that I'm older and look back on it things really were not that bad compared to what I have dealt with after getting out.
I didn't hunt at the time so that really wasn't a factor for me.
There are probably message boards for different posts and bases you could get on to find out what was available in what areas. Probably not much big game hunting opportunities in Iraq though, at least not deer anyway

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Paul