Annies pretty much rule the 3-P target world. The least expensive ones that are set up for the game you want to play are still excellent. Check them out at: ChampionShooters.com . Watch out for sticker shock!!
The Kimbers from CMP are gone, except for "new" but RUSTY ones, which may also have rusty bores.
Triggers are important to good position shooting. I wouldn't try to use a Savage MKII for 3 Position shooting; they just aren't well set up for it. If someone wants to shoot informally, like in turkey shoots, plinking, or recreationally shooting from the bench, the Savages are great. I haven't seen many wins by them, even in (unsanctioned) Plinker divisions of IR50/50 benchrest.
CZs are very nice rifles, but also not in the 3P or benchrest league, at least without a lot of work.
The least expensive quality target rifles are probably used Rem. 540X or 40X. The 540X may need to be bedded for its best accuracy, but triggers can be replaced.
Others, including the Rem 513 are pretty good shooters, but the actions and triggers are not the best quality. I had a Rem 521 that was an excellent shooter, but the action had issues.