A nice step up from 22LR would be 32 S&W Long. I plan to use wad cutters to get good penetration. Something like BB 100 gr WC for carry and I will use 71 or 85 gr plated reloads for practice; plated or jacketed required at my local indoor range, due to lead concerns. I have enough hand and wrist pain that that is getting to be my limit. S&W has announced a new Lipseys series of 32 and 38 cal versions of my M442. The 32 is in H&R Magnum, the 432 UC (ultimate carry). I tried a M43C, but had several concerns. Ammo reliability and suitability for defense, and a very heavy trigger pull, and after about 50 rounds, I had to clean the chambers. I think due to the cylinder being made of Aluminum and experiencing galling. The chambers were quite smooth, so that was not the problem. I needed a mallet to get ejection. 32 Long is probably the smallest reasonable step up from 22 LR, with center fire, for reliability.
For range use and home defense, women seem to like the M60 with a three inch barrel. My daughter learned on my dash 10 version in 1995. She liked the grip size and trigger reach. Could shoot standard reloads all day. I have medium hands and prefer the J frame also.

73,
Rick