Josmund,

Look for a quality design such as the older Winchester M70's that have CRF, and a mauser style action.

Avoid the entry level designs such as the 110 Savage and Rem 700's or 721-1's.

The 700's are known for accidental discharges caused by their triggers and there are many lawsuits. Nor do they have a three position M70 type safety that controls the firing pin.

Start with the 243 Winchester which is useful for varmints and some game.

Skip past the obsolete 222 as it's been replaced by the 223 which in itself is limited to varmints.