I have hit a 7" round target 9 out of 10 times with a .22LR subsonic at 300 yards...but that is only after dialing it in for the day. My 300 yard zero changes daily on my 22 because so many things change where it hits.
I shot 30 cal out to 300 as well, but not enough to be proficient with it. Just enough to know that it can be done.
I only shoot 22 cal now due to range availability and time. I'm a competition shooter (Olympic style prone - no scope, off of a sling & no additional support), shooting 25, 50 and 100yd.
On a good day 0.25 MOA isn't a problem at 100yd. Mostly 0.25 to 0.5 MOA at that range mind you.
Shoot a .22 well and you'll get a great foundation for any other rifle. I've gone on to shoot large cal up to 1200yd, but still find the requirements of small bore precision target shooting more challenging due to the ballistic properties.