I have eight Ruger 10-22's, all tricked out. And, I spent a lot of time on Rimfirecentral where I learned a whole lot about those rifles. It's a good place to learn about them.
The single most important thing you can do to improve the 10-22 trigger is install an aftermarket hammer. The factory sear works just fine, so no need changing it. I personally like the Power Custom hammer. Don't change the hammer spring either as the factory spring works perfectly with the aftermarket hammer, and factory sear. Beyond that, polishing mating trigger parts will smooth up the pull too. I'd suggest putting in a recoil buffer as it quiets the cycling noise a lot.
Cleaning the bore of the barrel using JB Bore Paste will improve accuracy too, about 100 strokes with a tight fitting patch loaded with the JB.
There are many other things you can do to improve the 10-22, but the hammer change is the most important change.
Shoot and enjoy..
Martyn