Small framed handguns are harder to shoot than a full-sized handgun. Generally speaking, they are recommended for experienced shooters.
Pocket pistol and sub-compact pistol can be one and the same.....or not. Depends upon who you speak to or ask.
I have a substantial collection, and in all of my handguns, only one I consider to be a pocket pistol. That's my AMT Back-Up in .45 acp. I also have a .380 S&W BodyGuard as well, but I think of it as a sub-compact for some odd reason.
As far as caliber goes, it's whatever floats your boat. You can ask 10 different people, and chances are good, you'll get close to 10 differing opinions.