Go to a big school the last thing you will think about is hunting.. Go to the best school you can get in. (we all know why state is full) j/k.
In real life people do care what school you graduated from.
You have the rest of your life to hunt.
I went to NC Wesleyan to play baseball and the small school thing SUCKED. Transfered to UNC the best years of my life no doubt. Met my wife, met some my duck hunting partners (some of us bought an impoundment together), met business partners and got one kick ass Job. You will get plenty of time on Christmas break to kill ducks. Plus as you get to be an upper classman you can set your classes so that you can hunt more.
If state is the BEST school you can get in then go to State you will not regret it. (Unless you don't major in engineering and apply for the same job a UNC grad is applying for).
Also Don't go to an all guys school (State is close enough).