asahrts,
Your thoughts on building your own target 10-22 are right on the $$$. You will be very pleased with any upgrade. I would start with an aftermarket barrel. Even a Butler Creek basic barrel, stock combo will give a 200% increase in accuracy over the basic 10-22. Throw in a recoil buffer and a custom bolt release and you will only have an extra 175$ if you shop, plus you will have the added satisfaction of "building" a custom rifle. The money saved can be added to the purchased for a scope.
Don't forget that the correct ammo is one of the big factors in getting a.22 rimfire to shoot bug holes, most .22's respond well to subsonic loads, Agulias' Super Extra are Ely primed and sell for 1/2 of most match 22 ammo. But all barrels are different and what works well in my 10-22 may not cut it for your "custom" build.
Once the barrel is replaced then you can, go for a custom trigger and sear, or maybe replace the complete trigger group with a Volquartsen, or Clark unit.
Every custom option on the 10-22 will usually give accuracy results, although some of them will have to be measured in 0.100 inch!