i'd go with a RUGER 10/22 HARDWOOD STOCK for roughly $280-300 A LEAPERS UTG 3-9X32 for roughly $150 and i would personally add a ATI stock for $129 so around $60 above budget.
it would look like something like this with this scope (btw it's a really good little scope i have one on my 9mm not too long or bulky looks great on small firearms )
Pic of my 9mm with the scope on