A good sized adjustable rear sight will probably allow you to see the sights & hit the target better.
The adjustable will let you fine tune to your target. And that will be more satisfying to a new shooter especially.
The bearcat sights are pathetic & seldom regulated properly. I have one & like it, but that's my experience with them. Of the single action type the Single Six has a nice adjustable sight.
When sighting the best way to do it, but not what you are inclined to do, is to focus on the sights & let the target blur out. (Yes I did edit what I originally said.
I'll blame it on not having had any coffee yet)
Or get a gun that you can add a low or no power scope to or a red dot sight. If you find you can't master the open sights after a while, you could add one.
Shooting offhand takes a while to master. Try also to shoot from a support so you can guage the actual accuracy from your gun and then you'll have a benchmark to shoot for.
.22's can also be finicky about ammo, so try a number of brands. After you get the feel of the gun, keep some records of groups. Best if done from support.
If you have access to a commercial range sign up for some instruction & you should get a good overview of stances, sighting technique, safety (remember Jeff Cooper's 4 rules of gun safety & you can't go wrong). If not & you're someplace you can shoot, set some targets up & blast away. Reactive targets like spinners or clay pigions or cans add to the fun.
It's lots of fun, but serious business too. Be safe & join the NRA.