Varmit target

[centershot]

If you buy a used rifle in great shape or re barrel one, if you stay with a .22-250, don't shoot it too hot or you will be in the same boat again. I use the temperature indicating tape on the barrel from Amazon or Mc Master Carr. A .223 with 40 grain bullets will approach what you are trying to do.

 

[redrockranger]

Stay a Remington guy..... Without being able to bore scope a used 22-250 i'd be vary wary. It could turn into a money pit.
The 223 would work better for a young man just starting. Inexpensive to shoot compared to a 22-250,brass readily available. A faster twist barrel could extend it's range.