What rifle does the barrel fit?
Yes the Magpul stock will fit so will many others.
Do you have a 1022 receiver ?
I found it strange you asked for specifics but provided very little detailed information.
A 10/22 off the shelf, better trigger and go from there. Many ways to go. Look at the top of forums at custom 10/22s and see what strikes your fancy. Good luck.
Rimfirecentral .com has lots of information on 1022 builds
I bought a stock ruger 10/22 to biuld off.
After pulling it apart I scraped that and went all in.
Full Dlask/Kidd stuff down to the trigger pins.
Put a hogue stock on it.
Very easy to assemble. Shoots 1/2” with cci SV.
Was a bit of coin but glad I went all in when I did.