The Civilian Marksmanship Program runs a class of competition that tries to limit how much can be spent on gear, the competition called ".22 Sporter", held during the Nationals at Camp Perry and some other places. That match will be July 22 at Camp Perry:
http://thecmp.org/wp-content/uploads/20 ... r=20180322
http://thecmp.org/competitions/club-san ... e-sporter/
http://thecmp.org/wp-content/uploads/Ri ... r=20180406
I have had three rifles modified for that match at Perry according to plans I saw on Rimfire Central (AKA RFC):
https://www.rimfirecentral.com/forums/index.php
As discussed above, the usual 10/22 trigger is awful. There are several vendors who specialize in modifying the factory trigger to one that feels good when the sear trips, and is any weight you want (I want them at 4 pounds for .22 Sporter). One vendor I have used is Brimstone:
https://www.brimstonegunsmithing.com/co ... uger-10-22
There are other vendors who will make a whole new trigger group for you, and they are generally excellent.
I found the biggest improvement in group size came from having the rear of the barrel faced off by .200" and the barrel rechambered with a tighter reamer, one which had the Lead bullet engrave in the rifling a little as the bullet was chambered. Slight engraving of the bullet will give the bullet support on firing. Too much engraving will give you slam-fires. The barrel on the 10/22 is no problem for anyone with an allen wrench set to remove and mail to a the gunsmith. It is also no problem to reinstall when returned, you just need to have a .200" spacer in the clamp. The 'smith that did this for me later stiffed a lot of people, so I won't recommend him. The smith that gets the most positive comments on RFC is this guy (he also reworks trigger groups and bolts):
http://www.ct-precision.com
Mention above was made of the odd way the 10/22 bolt leaves itself when your magazine is empty. There is a cheap modification one can make to the bolt stop, which is mentioned above, but it still seems odd to me. There is another alternative, but it is expensive, and that's the way I went:
http://cstmtech.com/10-22bs2g/
This has a mechanical sensor and a new 'blueprinted' bolt, and together they hold back the bolt after the last shot is fired. In my estimation, this is how a semi auto rifle should function.
A factory 10/22 is set up to work with cheap 10/22 ammo, which is high speed. High speed is rarely accurate. Standard velocity, even the lower priced stuff, is much more accurate, but the factory 10/22 is not reliable with standard velocity ammo. In order to make a 10/22 reliable with standard velocity ammo, it helps a lot to radius the bottom, rear of the bolt, so the hammer does not absorb as much energy when the recoiling bolt rides over it. While one is having this done, one can have two other things done to the bolt: set headspace tighter and have a transverse pin put through the bolt above the firing pin to keep it from occasionally kicking upwards, which is supposed to give squirrelly ignition. I believe the blueprinted bolt used with the CST bolt stop mentioned above has had all these things done to it.
One of the posters above complained about 10/22 stock length. I think they were complaining about it being too short. One thing I did was get a Mini-14 recoil pad, which has the same type of musket buttplate, and install that on my 10/22 rifles, for an inch more length.
Having done all these tweaks, I usually have no difficulty shooting a perfect score in slow and rapid prone at 50 yards with a scoped rifle. I come close to that with Open sights.