Call me +3 to the other comments!
Rifled slugs are good to go and Oli gets the gold star this round!
As to the distinct differences in load type;
Birdshot is for bird and small game generally and rather not adapted or suitable as an HD load. (There is way more info dedicated to this in the ammo section)
Buckshot, generaly 00 or #1 is considered acceptable as an HD load. Buckshot can also be an effective load for coyote, wild dogs, and deer within range, though many brands I wouldn't be comfortable pushing beyond 25 yards.
Slugs at typical HD ranges are too much for me to be comfortable with. From what I have seen, they tend to retain weight and shape much more so than I used to believe. This may allow the slug to penetrate and continue penetrating after initial impact with the intended target. Generally 25 yards and beyond, I'd rather be loading a slug for reasonable accuracy and reliable stopping power and far better chance of humane kills if I'm hunting.
Now to shell length.
I personally have zero desire to test 3" shells. It isn't IMO worth the loss of capacity in an HD or competition gun, and I haven't seen anything performance wise to warrant switching over to 3" as a hunting load, especially given the added recoil.
Most importantly in your search for a favorite load(s), never take my word for it! Go shoot A LOT!!! See what meets your needs and see what you like!!!