I went with a Kidd threaded 10" barrel for my 10/22 SBR. It is very accurate but weighs a lot. I wish they made a fluted version. I am investigating some reliability issues but the source is most likely the modifications made to the bolt assembly.
For super quiet, a integrally suppressed barrel is an option, and there are several aftermarket manufacturers of quality bull barrels and sporter barrels to wring out the accuracy, also a bunch of trigger groups to go with. Budget minded is the Ruger BX trigger for $80ish, and up to the KIDD or Volquartsen trigger groups around $2-300. They both make barrels, as do greenmountain and others. Try checking out www.rimfirecentral.com for tons of info and reviews on all things rimfire and 10/22.