For that I would go with slugs or if up close and personal 00 buckshot. Personally I would stick with slugs.
#4 buckshot should work well for varmints like coyote, feral dogs, and the 2 legged variety, out to 20-25 yards or so and shot placement would not be as critical, but still it's hard to beat a well placed shotgun slug for changing someones mind. Once you get out and shoot your 20 gauge (I suggest you AVOID 3" shells and stick with 2 3/4" standard shells) I think you are going to like it. Get some inexpensive 2 3/4" Remington sluggers or more expensive Remington Buckhammers ( 2 3/4"also), some 2/ 3/4" 00 buckshot, some 2 3/4" #4 buckshot and perhaps some low brass # 6 or 7 1/2 shotshells a go out and experiment with it. The Tamer stock is not the best at reducing recoil, so if you can get a slip on recoil pad (a Sims medium perhaps) get one, you will thank me. You might also try out a regular H&R/NEF rifle/shotgun buttstock on it. I think the best would be a straight (non Monte Carlo) synthetic buttstock, they come with a recoil pad, or perhaps a survivor stock with a slip on Sims pad....<><....