I had kept #4 buck in my HD pump for a long time. Inside the home and at short range, it's a fine round. Recently however, I have switched to #1 buck for my first couple of shots, followed by #00 buck. I never see #1 buck at my local sporting goods stores, but it can be found online.
I began to reconsider #4 buck after reading an account of a police officer, who used this shell in a shoot out with a bad guy. Long story short: the bad guy was hit center mass at 35 - 40 yds. The bad guy was wearing a heavy leather jacket. Not one pellet penetrated into a vital organ.
Now I don't think it prudent that any civilian follow a bad guy outside of your home. Make sure your family is safe, call 911 and wait for the Calvary to arrive. But after reading that LEO's account, I thought a shell with a slightly larger and heavier pellets might be the way to go.