I'd suggest going to a range that rents guns, and try out some single action and double action revolvers and see which you like best.
Double action .22's tend to have heavyish double action triggers in order to reliably light off the rimfire rounds.
Shooting a double action revolver in double action mode is a very different experience than shooting a single action auto-pistol like the MkIII Ruger.
Get good with a double action revolver, and you'll likely be able to shoot anything well. If you really want to devolp good trigger skills, this would be a good investment as the cheap ammo will give you lot's of "trigger time". You can cock the hammer on the SP101 and shoot it single action, but it's a different experience IMO, than shooting a dedicated single action revovler.
The Single Ten is a great gun as well, and the feel and ballance of them is quite nice. These are a ton of fun to shoot , but not everyone digs single actions. The are slower to load and unload than a D/A but many of us (myself included) like the take your time approach of the S/A revolver. For longer distance shots, the longer sight radius of the Single Six/Ten and lighter trigger will be an advantage. The trigger will feel sort of similar to the MkIII as they are both S/A's
Both are nice examples of their particular style of gun.
Myself, I shoot a Colt Officers Model Target for a D/A .22 and on Old Model Single Six for a S/A .22 and love them both.
I can't say which one you'll prefer, but either way you'll be getting a pretty nice revolver.