Honestly, sell both the barrel and stock for $60 and buy a $300 basic 10/22. You’ll come out ahead without the hassle.
ETA: You've already said you want a different stock, so effectively you're starting with the barrel. At best, the OEM barrel is meh. It's designed for maximum reliability rather than accuracy. You can send it out and have it tuned for $60 or something, or you can buy a better barrel for $100.
You might be able to piece together a rifle for less than $250, but it will be hard. There is a reason people buy a new rifle as the basis for a build, sell or throw away the stock and barrel, and use the other parts to build what they want.
And with a new build you *really* run the risk of wanting slightly better parts and wind up with a $600 10/22. Ask me how I know...
ETA: You've already said you want a different stock, so effectively you're starting with the barrel. At best, the OEM barrel is meh. It's designed for maximum reliability rather than accuracy. You can send it out and have it tuned for $60 or something, or you can buy a better barrel for $100.
You might be able to piece together a rifle for less than $250, but it will be hard. There is a reason people buy a new rifle as the basis for a build, sell or throw away the stock and barrel, and use the other parts to build what they want.
And with a new build you *really* run the risk of wanting slightly better parts and wind up with a $600 10/22. Ask me how I know...