Last winter I shot my first Bullseye league with a standard 4" Ruger Mark II. Before I was mid way through the league, I'd installed a set of Hogue grips and a Trapper spring kit and my own work to the hammer and sear. Volquartsen trigger too. Toward the end of league I purchased another Mark II in Slabside Stainless Target model. One evening I transfered the internals from the old shooter to the new. Then I sold the standard model. My scores went up with each upgrade. Now I've made the slabside even better by drilling the frame and threading in a trigger pre-travel set screw. What a difference. I like it so much that here on THR I purchased a 4" Bull Barrel Stainless Mark II with Clark trigger and Volquartsen Vcomp. I've made the same internal changes to this pistol. And I've added a RedDot to the Slabside. I'm getting used to that, but so far still prefer open sites.
http://www.cnw.com/~hotrod/Toys/GunStuff/SlabSide.JPG
http://www.cnw.com/~hotrod/Toys/GunStuff/4inchBull.JPG
In my eyes, the Ruger is about the best for an entry, middle of the road pistol for competition. (New, a Slabside Stainless Target model is over $400). Now I know there's a lot of support for the Buckmarks. And out of the box they are fine plinkers and target shooters. Out of the box, the trigger is better than a Ruger. But there's not much aftermarket stuff for them. And so much available for the Ruger that the Mark II wins. Hamerli's and Pardini's are really nice. Nice and spendy. There are people in our club shooting 550-570 (600 series), with Rugers, Brownings, Smiths, and one Sig/Hamerli. One vetran shooter with a Pardini, (her Hamerli sits in a box), and her scores aren't any better than the cheaper pistols. Oh, and price a Sig/Hamerli Magazine. Buckmark mags aren't cheap either. A plus for the Smith, 1911 framed conversion, Buckmark, or the Mark II, They'll still fit in a holster for grouse hunting with your boys. I've not seen a holster for a Hammerli or Pardini.
Do an Internet Google search for "Bullseye shooting". There's a plethora of information there for centerfire and rimfire Bullseye.
Contact your local club to see if they have a Bullseye league.
My local club also has Falling plates and Pin tops competitions with rimfire classes.
-Steve