As a single shot bolt action, specially if someone wants to get into competition shooting, check out rifles like from Anschütz, Walther or Feinwerkbau.
Here an example at gunbroker.com
Heavy match grade barrel, match hair trigger, 11mm prism mount for Diopter or scopes.
We have three such rifles in my gun club and they very accurate bastards.
It`s just a matter of pricing. If you can find a dealer in Germany that would export a rifle to the US, you can get very good bargains partially for less then € 200,- for the rifle.
Check out this link to a german firearm auction plattform: