The MKII is one of the niftiest guns made, and my personal favorite. It has everything that makes a Ruger pistol great, and nothing it doesn't need to make it drag. I've got a Government Model MKII with a heavy barrel. As-is, with no modifications other than "activating" the factory target trigger. Lots of folks are unaware that target model MKIIs have such an installed provision in their gun, which is a very nice, creep-free adjustable trigger. It just requires that you adjust it, as it was usually left alone by factory personnel, feeling like a standard trigger. The Government Model was made with very tight specs, originally for US purchase, and then to the public, and is for the most part the forerunner of the Hunter MKIII, sans barrel flutes. My favorite addition was the combination Hunter-style V-notch rear and lite-pipe front sight. This pistol was made to deliver mil-spec accuracy or better, and mine is the latter, a lot better.
If you've a standard MKII that lacks that trigger provision, follow North country gal's recommendations. I've done a lot of experimentation with ammo of many types and sorts. My personal favorite that I use in .22 bowling pin competition has been Federal bulk pack. It kicks the sawed off tops clear of the table by 8 feet, and shoots into 1/2 inch at 25 yards. For greatest accuracy, CCI Green Dot, Federal Champion, or CCI Mini-Mags are even better.