@Truth teller: "Franken" always has good advice. I live by his words. However, like real estate, used guns seem to be driven by location and market conditions. Here in central texas, the local gun shops don't have a lot of used bolt action 22's, and the ones they do have, look like they've sat in a barn for 5 decades and cost only about 50 bucks less than the price of a new one. But (as franken said) a used gun may be your best bet if you're lucky or if you can find a good deal from a private seller.
At the end of last August, "Aguila Blanca" (a moderator and staff member here) posted a thread asking essentially your same question. It might be helpful to search for that thread by the original poster's name (Aguila Blanca) and review his thread.
If you go for a new rifle, the only thing cheaper may be one of the mini single shot bolts (Savage rascal), but I don't think you would want that. In the 200 to 300 dollar price range, you would get, in order of increasing price: the mossberg plinkster, the savage mark II and the winchester expert 22. (And I didn't realize that the mossberg was a re-badged rossi.. thanks franken.) Beyond that you get into the ruger american, CZ 457, and then ultimately the bergara and tikka, followed by an Annie (anschutz) and Christensen. I think Christensen is now offering 20 year financing with a buy down on your interest rate. /s.
You may want to consider the winchester expert 22. It's not really a winchester. Instead it's a re-badged turkish gun, but it has good reviews on you tube. Plus the winchester uses the ruger 10 shot rotary magazine, which may be a desirable feature since you already have a ruger 10/22. Anyway, good luck. Half the fun of a new gun is the planning and finding stage.