I've been tossing this idea around myself. I have enough (well, for now) big dog rifles and I gave my wife my other custom 10/22 when I got my CZ bolt .22.
Accuracy is going to come down to 5 things:
1. Shooter
2. Trigger
3. Barrel
4. Ammo
5. Optics
From there it just depends on how small a group is small enough, and how much you are willing to spend to cut .125" off your groups.
Like others have said, the 10/22 is a grown ups version of Legos.. there are a million parts to soup it up to whatever style/config you desire.
For me:
Stock: Traditional hunting stock or a Tacticool (have on my CZ and like).
Barrel: Probably a Clarke or Shilin medium profile (I'm over the bull barrel thing).
Trigger: Probably a Kidd kit (Did Volq parts on my wifes and always did well too)
Ammo: Nice thing is the higher end stuff hasn't changed price much, unlike the 500rd bulk packs. Wolf/Eley/Lapua work when you find the right one. Again, how much are you willing to spend to shave tenths of inches. And in reality.. If you could get 50 rounds of Olympic Match quality ammo for $30, wouldn't you?
Optics: No comment as this could get ugly.. I'll take clear glass over power any day.
****! Now I want to start a build..