It all depends on your budget and what you want to use it for. I use mine for paper punching and occasional ground squirrel. I have one with a simmons 3x9, one with a Weaver KT 15 and one I just removed a Nikon Monarch 5.5x16.5. I bought a rifle with a leupold 24x to rob the scope and put on the 10/22. I would recommend a trigger upgrade as first order of business. All three of my guns have a volq. trigger kit and .920 barrels. For all around scope hard to beat a fixed 4 or 3x9 if you want more magnification.
I do have a rare finger groove model that wears a weaver K4. But I think Im going to sell the stock and barrel.
Whatever you get, you should consider these issue.
Rimfire ranges are shorter than centerfire, and rimfires tend to be shot at close ranges for plinking as well as hunting. Many centerfire scopes will not focus properly or have proper parallax adjustment.
So, here are two criteria in selecting a rimfire scope.
If the objective is not adjustable, look at scopes specifically made for rimfires. These will have the fixed objective factory set to a closer range. Shotgun scopes will also be set closer, but generally they will have overly heavy duplex reticles.
If the objective is adjustable, most cut off at 50 yards. Try to find one that adjusts closer. Those made for rimfire will typically go to 10 meters (33 feet) because they are also set up for airguns or 50 foot range shooting.
The above is not a huge issue with low powered scopes, but if you are using a 2-7x or a 3-9x etc., the higher magnifications will show this to be a big issue.
As for the scope on my 10-22T, it's a Leupold Vari-X II 4-12x, with a 40mm adjustable objective. It has served me well for two decades on that gun. I consider it to be ideal for the 10-22. Low enough magnification for fast shots close up, and the 12x is nice for precision, or for testing ammo groups at the range. It's not exactly a cheap scope, but it is affordable. Also, Leupold also makes a Mark AR 4-12x that has a target elevation knob. I'm tempted to install one of these instead, because I often shoot subsonics though a suppressor and the target knob would make changing the POI much easier.
I like my Mueller APV 4.5-14 40mm with adjustable objective. It cost me $115 from gunkings.com. It is on my 1022 with the GM 20" steel .920" barrel, Hogue Overmolded stock, Kidd receiver and bolt, and Kidd two stage trigger.
My steel gun is a 1022 with a Tactical Solutions 16" aluminum shrouded barrel, Boyds thumb-hole stock, Kidd single stage trigger and a C-More red dot.
Both guns are extremely accurate and very reliable.
The Leupold products are very good and I am a big fan of that equipment. More recently though I have been buying Nikon scopes and I tried one of their Prostaff 5 3x9s with the 150 BDC reticle on a Winchester M61. This scope is designed specifically for the .22lr round. What a great combo on the M61 and it really lets you maximize the field potential of the .22lr round. I think these scopes are a very good value and don't consider them to be a compromise to the Leupold products.
In addition to that, also consider getting one of the electronic red dots for some real fast action shooting. Tons of fun and just the ticket for running rabbits or just bouncing a pop can around. They don't cost much and if there ever was a plinker that screams for a red dot, it is the 10/22. The only problem with that set up is you won't be able to keep your magazines loaded.
Volquartsens trigger kit, nikon rimfire scope with the 150bdc reticle and i have a boyds stock on mine, it also has a anodized aluminum barrel with the steel barrel sleeve. I shoot CCI velocitor ammo, it knocks the snot out of squirrels from ranges unheard of for a .22. Call scott Volquartsen and get a trigger kit before you do anything else. I installed my kit at home and of course i had something wrong with it. I called Scott and he had me send it to him, only cost me the $20 to send it to him and he had it back to me very quick, it helps they are only a couple hundred miles from me. Ill try to post a pic on monday. Good luck the addons are unlimited!!!
I have one of the Nikon Prostaff Rimfire 3-9x40mm BDC(mildot) scopes on one of my 10/22's. Do not overlook this scope. It is a very clear scope and is very well built with optics that I swear rival some of the much more expensive scopes. It also has plenty of power for rimfire use and the price will not break the bank.
I have an old Burris fixed 4x on another rimfire rifle of mine. These old scopes had excellent optics with a nice clear picture across the whole lens.
+1 and +1 for the Leupold Vari-X II 4X rim fire special. I have one on my 10/22 and another one on my Marlin 39AS. These rifles are set up for hunting. These scopes have finer cross hairs than the regular Leupold high power scopes. They are super bright, have lots of eye relief and a wide field of view. Plus, they are compact in size and look better when mounted on a smaller rifle.
The Leupold Rim Fire Special is a rugged scope. I had one mounted on a Marlin 336 in .35 Remington for a few seasons and it took a couple of medium sized bucks. The fine cross hairs take a little getting used to but they get the job done.
For paper punching, on either the 10/22 or a 77/22 varmint, I use a Leupold 6X18 AO with a dot reticle and target turrets. I lap my scope mounts so I can move my scopes around without bending the tube.
I have a 1980's version of the Leupold Vari-X II 3X9 AO that I don't use any more. I may try it out in the spring on the 10/22. The Adjustable Objective feature really makes a difference for a rifle that is shot mostly at 50 yards.
Most high power rifle scopes are set to have minimum parallax at 125 yards or so. Scopes for .22 rifles are set to have minimum parallax at 60 to 75 yards.
I don't know what a current Leupold Rim Fire Special goes for but I paid about $150 each back in the mid 1980's for the Vari-X II version.
For a few more bucks, there is a 2x7 version. For hunting, a 4X is fine.