What range do you stay in?

It will heavily depend upon the terrain/location and rifle/bullet load/scope. Plus, people will usually overestimate.

In the southwest, they sometimes will take a shot at 400 or more yards (my hunting partner originally set up her rifle for being able to take a 1,000 yard shot for that area), because they have to. On the east coast, they're usually shooting well under 100 yards, so deer slugs are both the norm and the only legal round. Most standard sightings have a rifle at zero at 250 or 300 yards, and rapidly dropping off after.

A 400 yard shot, with a rest/prone and lots of practice is very possible on a still target with the right round. It's certainly a better shot than shooting at a deer running at full speed at most distances.

Edit: Oh, and my first year hunting too, since I was young. I went for a neck shot on a still target at 150 yards or so and got it. Much more and I would have certainly gone breadbasket. I don't think I would have been comfortable taking a shot at 400.

Your post has lots of questions, so with almost 50 years of hunting behind me here's my best attempt to answer: The most important factor in determining how far out to shoot at game is YOUR own PROVEN ability. By that I mean how far out you have practiced before hunting season even begins. Regardless of what rifle (or bow) you shoot, it's the HUNTER"S potential that really matters. If you have a gun/scope combo that is capable of shooting accurately to 500 yards, but you've never shot it consitently accurately beyond 150 yards, then that (150 yds.) is your limit with that rifle.
You can never be too prepared when it comes to shooting practice. My typical shot for elk, deer and antelope probably averages between 150 and 200 yards, but I practice out to 430 yards. (That's as far as our club's target range goes.) Even so, I would only take a shot at that distance if everything is just right: good rest, little or no wind, broadside shot, animal not moving AND the confidence to know I can ethically take this shot.
So, how far away was the ten point whitetail that I shot this year - just about 50 yards and still coming toward me when I pulled the trigger.
One other thing that hunters overlook in long range shooting is range estimation. By that I mean even if you have practoced at, and can reasonably take a 200, 300 or 400 yard shot, but you have no idea of how far away your animal is, how in the heck would you know where to aim?
I have an article called "Long Range Shooting" that you might want to read which covers this subject in great detail on the home page of this web site under "Recently Added Tips".
Gromky, not to be critical, but I'd advise against those neck shots. I know just saying this can start a lot of debate because a well-placed neck shot will drop a deer like a sledgehammer. But at any extended range, it's really tricky. Unlike other aiming points, there is no margin for error with a neck shot which makes it a lot easier to wound an animal. I have the best luck with the high lung shot. If a little low, you can will hit the heart; a little high, you brake the back; a little forward, you brake a shoulder; a little back and your bullet hits the liver - ALL still very lethal hits. Good hunting.

Thanks for the replys. Lots of interesting information here. But I have a couple of more questions: What percentage of your kills are on the move? I had a deer moving at a slow gait in my sights a while back and was comfortable with the shot but my safety was on and by the time...you know how the rest goes. Anyway I was comfortable with shot but only because it was within 100 yds, it was a broadside shot, and it wasn't exactly running. Anything else and I wouldn't have wanted to pull the trigger.

And how do you hold a gun when you fire it? I know having the barrel resting on a log or something else solid would be best but I haven't been in that situation yet. So I just rest my elbow on my knee in a kneeling position. Otherwise there's too much movement. Anyone steady enough to shoot accurately without support of any kind? How do you do that?