Well, as
@MacAR just related, a .357 Magnum is
light for possum, so I'd go larger 475NE at a minimum.
Or a golf club.
I was cautioned in that thread to use nothing less than a 500 NE.
In all seriousness, I usually use a 22 since I don't care if it runs off and dies, and I like to watch the acrobatics. Plus, its a lot quieter at 2 am. My Single Six has accounted for several in the last few weeks. I used Federal HP', and they were all one shot kills. On the other hand, I now have a .22 caliber bullet hole in my shop wall from an armadillo. My aim was a bit high, and the bullet bounced off the shell and went through the sheet-iron wall. Luckily nothing was damaged.
So, with that said, I recommend a shotgun. I shot 6 'dillos in one evening while on a walk. I used a single shot 410 and 3" #6's. Worked a treat, and all were pretty much drt. I admit that I "snuck" up on them and the range was quite close; twenty feet or less. For what I call "yard work", I use this:
This old M24 Winchester is a side by side 16 gauge built in 1939. I keep it loaded with high brass #6 shot. They don't move, twitch, nada. DRT every. Single. Time.
Bottom line, if I were you I'd use a shotgun unless I had close neighbors. If that's the case, I'd use the 22. Quiet, but not so quick as the scatter gun.
Mac