I would say that any of the Mark II target pistols would do nicely.... try before you buy if possible. If you have the chance to try a few different models, you may develope a barrel weight/length preference.
Try both the steel frame & 22/45, the grip angles are much different, I have had both, but my favorite is the 22/45 with a tapered 4.75" barrel & fixed sights, I like the weight (26 oz) and the balance
The steel frame 5.5" bull barrel is probably the most popular for most people, but my taste is usually different, (I owned 6 Chevy Corvairs and loved them!)
The grip angle on the Mk III is probably more suited to single-handed bullseye shooting - the larger grip of the 22/45 is more suited to two-hand Weaver-stance shooting. If you like the 1911 style grip and controls, the 22/45 is the right gun. You'll also find some weight differences, so try them out to see what you prefer.