I hunt a lot of public areas and my son shot his first couple deer off them during youth hunts. My advise would be scout ahead of time like was already mentioned, but also check the type of public land. People like to use it as a blanket statement and if they get a deer its some sort of validation of being difficult I guess. Truth is though, there is a wide range of public land and each one has slightly different rules. If you want to use a treestand for instance, some allow it all season long, some you must remove daily, some need names, etc. This will all vary based on if the public land is Federal, state, county, MFL, etc. There is no one rule that fits all.
The youth hunt isn't usually bad in terms of people either. Some archery guys avoid it (plus its beginning of Oct, not the rut yet). It won't be anything like the 9 day season. I always thought of it as archery hunting with a rifle.
When we first went, I didn't focus on getting a buck. I thought about where the highest chance was for us to see any deer. My son was going to shoot the first deer he saw, so I just wanted us to have the highest chance of seeing anything, even if it was just a doe.
Finding private land is tough these days, not like years ago. Deer make people very weird and possessive now. Tends to be the crux of every deer related discussion when you get down to the root of it.