I was going to say this^ but dsink beat me to it. The Flite Control shot cup paired with 00 lead shot is the best thing going for any kind of shot. I get 4-6" patterns at 20 yards with my 18" Imp Cyl barrel. (870 Police Magnum)
I have used this load on coyotes, deer, pigs, and raccoons out to 50 yards.

I greatly prefer slugs for bears and deer, but you asked about SHOT, and that is the best SHOT around for critters bigger than groundhogs.

If you want to talk about SLUGS, we can have that conversation also. (Hint, it rhymes with fennekkee.)