I hunt public land in gun season, and have for years. Wear orange, be aware of your surroundings. For finding deer, I look for the sign and then hunt it. Ya, you can go deeper to avoid others, but there may not be any deer there. The best combination is lots of sign in an area others can't or won't get to. One of my best spots for public land was an island cut off by a lake, and two creeks. You could get there by canoe, or crossing a really sketchy log across the creek. I used to hunt in there and saw lots of deer. When the shooting starts they head to places they know are secure. I like to hunt swampy areas on public land too. it's thick, wet and nasty so allot of people won't go in. But the deer are in there. Give us some more info, like what state you're in, and what the terrain is like.
-Jake