I purchased military trainer rifles from the CMP for use in competition. Prices for the M52 D’s and Rem 40X’s are way out of your price range. I estimate that an all correct rifle will be $800-$1200. The best of the “affordable bunch” are the Kimber M82G’s and the H&R M12’s. I am of the opinion the H&R M12 is the better built and better design, being a product improved M52D.
I shot these groups in competition, prone, with sling, at 50 yards with my M12.
The Kimber is an excellent competition grade 22 right out of the box.
I believe the diamond in the rough is the Stevens M416. This is a WW2 era rifle and was an excellent medium priced 22 LR. It was not a cheap or cheaply made rifle: in 1939 the cost was $28 but adjusted for inflation, that is $455.00. It takes work to find rear sights as the front and rear sights were removed from the CMP rifles. A Lyman front sight works perfectly with the period rear.
Based on limited shooting, I believe a good Stevens M416 will hold the ten ring and maybe the X ring. These early rimfires are more difficult to shoot against modern competition rimfires as there is no adjustable handstop, and, similar to the Kimbers and M12's, the buttplate is not adjustable for length and the cheekpiece is fixed. But, as with the other rifles, it met the small bore prone rules of the day. The Army believed in aimed fire, supported competition sports only because they believed these events would train potential draftees to shoot accurately in combat, and the Army wrote the NRA competition rules so that the rifles that were not that much different in ergonomics to M1903's and M1 Garands. Small bore competition rules stayed Army retrogressive until the late to middle 60's when the Army disavowed the concept of accurate long range aimed fire and stopped financial support for the National Matches.
Stevens M416