I know you say a .223 is out of the question and I'm sure you have your reasons for saying that. However, a new or used .223 in a single shot like an H&R or Rossi, or bolt action like the Stevens 200 and Savage Axis isn't going to be anymore expensive than some new rifles in the rimfire choices mentioned. Just be patient and wait for the right deal to come along and you can step into a centerfire cheap.
Ammunition for the rimfires can cost your around $13-18 for 50 rounds of premium loads. I realize that .22 WMR can still be had for less than $10 a box of 50 rounds but that is for plain old TMJ rounds and 40-50 grain plated and unplated lead bullets of either the RN or HP variety which wouldn't get you much more usable range than the .22 LR. You can get .223 ammunition suitble for your shooting needs for around $6 for 20 rounds so in my eyes the cost of shooting is a wash.