The Anschütz 54 is a military trainer designed following the tradition of German rimfire training rifles from the Third Reich. The DSM was used during that period and good specimens are beyond your posted budget, the Anschütz is borderline. It is built on the famous 54 match action, inspired by the Mauser 98 action but reduced. It finds application in .22 Magnum, .22 Hornet, and .222 Remington.
There are a few trainers currently available like the Romanian M69 and a polist trainer. I want to again recommend to you to get over on RFC and get some info on your subject of interest.
A good Anschütz starts around $800 - 1,000.