BSA is the answer.For most .22 use inside of 100yds I like a decent 4 power shotgun scope. Fast to aim, wide objective, good eye relief, bright, not "overpowering". It just works good, but I recently went with a 3-9 variable and it works well also. Plus I can adjust the power. Most brands in the 40-70 dollar range are decent enough for a 10/22. Under a hundred? There are tons of quality manufactures of scopes in that range, just gonna have to find one that fits into your plans of use.
I actually bought an NC Star scope used. It's an ultra short 3x9 tactical model for an AR. About 6" long or so. I think I paid $25.00 for it with rings. I put it on a 10-22...pretty good scope.Check out inexpensive NC Star scopes. Plenty tough for a .22lr. Many of them come with milling type reticule. Even if you never measure anything with your milling reticule, the ability to use the milling dots as holdover points is awesome. Especially with all of the bullet drop that a .22lr has.
I've got their 4x and also a 6x compact rifle scope with the p4 sniper reticule.I actually bought an NC Star scope used. It's an ultra short 3x9 tactical model for an AR. About 6" long or so. I think I paid $25.00 for it with rings. I put it on a 10-22...pretty good scope.
Do more research. For a .22 out to 100 yards, a BSA is just fine. A cheap 3-9 Weaver would work fine too. Don't spend more than $100. Anything more than that is a waste of money, for OP's purposes.I'd do a little research on scopes before dropping any cash, as optics are one of those things you really don't want to skimp on. As I understand, BSA is widely considered so much junk, you can likely do better for around the same money.
Check out the optics section at other forums, like rimfirecentral and Thehighroad.org,for more info. Also,two great companies to purchase optics from are SWFA and opticsplanet.
For cheap Chinese glass, Mueller is by far you're best bet...