If you're able to zero it, then it jumps off target, it sounds more like a sight issue than the trigger. Make sure the scope rail is secure (not just the mount/rings, but the rail itself). The factory rail is not the best.
Then consider pulling the scope altogether and trying the iron sights to see if that's more consistent for you.
As for the trigger, Brimstone's lowest-level (less than $50 including shipping) is the best budget buy. It's actually at least as good as the Ruger BX, and I'd say subjectively speaking, it's better.
You pull your trigger assembly and mail it to them. About a week or so later, it comes back ready to install.
If you're willing to spend a little more, Brimstone's mid-tier job ($80-something with shipping) is even better, with a better (replacement) trigger design and a trigger stop. (Plus you can get the trigger in a fancy color if you want!)
They also modify the bolt release at all tiers.
The BX Trigger is much better than factory, but I wouldn't consider it the best option in the price range.
(It also annoys me that they don't put them in the 10/22 to start with.)
Interestingly, factory 10/22 triggers are hit and miss. I've had them from 5 to 10 lbs--both in aluminum and poly. Unfortunately, the design of the mechanism limits how smooth they can be made.