I used to shoot woodchucks with 3" 12ga No 4 Buck Shot through an Improved choke. It would roll them at 45 yrds. I found that anything tighter gave me too small a pattern when they were inside 15yrds and running through the grass. This was 20 some years ago, but I seem to recall the recall the recoil between mod and improved to be marked. I don't know what you've got for an auto, but I'd recommend gas operated.
I'd start with Modified and go from there.
