We had a Savage 22 target rifle (single shot with the thick barrel, and peep site) no scope, with the peep site at 100 yards you could pick off soda cans, a soda can on its side so you only saw the bottom or the top was a challenge, party balloons were no challenge at all. One time I tried to split a bullet at 75 feet on a piece of rusty angle iron with the point pointing at me. Split the bullet on the first shot leaving scrapes on the rust on both sides.
The trigger pull had a nice set-up for adjusting how hard it was to pull. For long range shooting I made it very lite. The gun started to go off if it was bumped with the safety off, safe handling caused those rounds to safely go downrange. I put the trigger pull back to 3 LB and it still happened. It turned out that the rear screw that holds the stock to the metal of the gun, was sticking up through the threaded hole so that it rubbed the bolt and caused the bolt to fire. Apparently as the wood wears the screw sticks through the metal below the bolt because there is less distance between the head of the screw and the threaded hole. I shortened that screw so it no longer sticks up high enough to touch the bolt. Something to keep an eye out for anytime you put any gun back together if there are any screws that have threaded holes near any part of the gun having anything to do with it firing.
Over the years many boyscouts qualified for the riffle merit badge with that gun, and several adults had fun plinking with it. I had site settings for different ranges wrote into the white felt of the gun case. For a tight group at 100 yards I used yellowjackets.
If you want an accurate gun in general you get more accuracy with a (single shot with the thick barrel). The next best would be a bolt action with the thick barrel. A semi-auto would probably be the least accurate.
If you are buying a used rifle and want accuracy, one big thing to test is weather or not the barrel has had too many rounds through it. I do not know how many rounds it takes to wear out a barrel, and it probably varies with the ammo used, and also how hot the barrel gets because of fast repeated shooting, verses being given time to cool. So if you are buying used, it probably would be a good idea to ask the previous owner who knows that gun what round is the best for accuracy, and then get some of that round and fire quite a few at the intended range to see if the barrel is or is not still good.