if it was me and i had to buy a shotgun for this purpose,i would go for the 12 gauge.and then you could go one step further and get a 3 inch mag.shot size is a matter of debate,buck shot has good knock down power and even though the holes will be bigger there will be less of them.this is a plus when looking to mount one,it will also decrease the odds of punching holes in the ears.on the other hand becouse theres less shot in the pattern your aim will have to be more exact on the animal.i believe its important to paper test any shot you want to use.somtimes smaller shot size will pattern much more even amd more centered then the larger size.every gun is different so test yours at the range.as far as slugs for coyotes,i have never taken one with a 20 but have with a 12 and let me tell you its not a pretty sight.i would have to guess even though the 20 is smaller,it still would couse more damage then nessesary.as far as range,with shot your limmited to 30 yards or so.with a 3 or 3 1/2 inch mag and full choke you could reach out there 50 plus yards.a scoped out slug gun on the other hand will reach out there 100 plus yards with a smooth bore and double that with a rifled barrel and sabots.your willingness to take the time to match a slug to your gun and your shooting ability will decide the final out come on exact yardage with slugs.shotgunning coyotes is alot of fun but one thing you must relize is,it has to be up close and personal.getting the eastern coyote to within shotgun range can be a diffacult thing to do somtimes.a rifle such as the 223 is more effective for coyotes and alot easyer but if you have the knowledge and skill then by all means give shotgunning a try.