It's a lot of fun and quite challenging to shoot 22LR at distance. My club runs long-range silhouette matches. We shoot metallic animal silhouettes at 50 m, 100 m, 150 m and 200 m. Typically the 50 m chickens are shot standing, but the longer distances are prone. With that said, this is a non-sanctioned "fun" match so some folks will shoot from the bench or use other schemes. The great thing is that it gets some of the older folks out to shoot. Some of them have trouble getting into prone position or aren't all that steady in standing anymore. No matter, they come out and shoot how they want and have fun doing so. Awards are not given, just bragging rights. And we only compete against ourselves. If I do better than last time, great! If not, I had a great time trying.
I use a CZ 452 Varmint with a Harris bipod up front and a monopod in the rear. The trigger in the 452 wasn't very good so I installed a Timney. I considered the kits to tweak the 452's trigger, but didn't mess with them. Scope is a 6.5 x 20 Leupold. The variable is nice since I can go 20x prone and dial down to 8x or so for standing. There was inadequate elevation adjustment for a 22 at 200 m so I mounted it on a 20 MOA base. The 22 slug is dropping rapidly at 200 m. For example, it drops about 18" between 200 yds and 200 m! Some of the 30 mm tube scopes have enough adjustment built in. YMMV.
Ammo is critical. I'm currently using Eley Target. It's not so much about being sub- or super-sonic, but muzzle velocity variation. I have proved with a chronograph that small velocity variations result in large vertical stringing at 200 m.
And then there's the wind. A slight puff will blow your 22 around, so you learn to keep on eye on the flags, the grass and the mirage. I'm beginning to believe that spin-drift is getting into the picture too. I have to click in windage at increasing distances - even in a dead calm. I thought my scope might have been canted, but I sure can't confirm it. So my sight settings include both windage and elevation.
I don't think you'll go wrong with a CZ. They're not hugely expensive and are very accurate. Sure, there are lots of alternatives. We had one guy come out with his 10-22 and a cheap 4x scope. He hit a few targets and got hooked. Then he said he was going rifle shopping. So my suggestion is get a bolt-action 22 that you can use a lot of different purposes. I'd advise against a plinker although some are astoundingly accurate. Get a good variable scope with repeatable adjustments.
I think you'll enjoy yourself!