Here are my tips, based on avoiding disappointments I have observed in others, or have experienced myself:
1. If buying to shoot, the condition of the bore beats all other considerations. This means if possible using a bore scope and/or bore gauges, not just a squint down the bore. Rebarreling is very expensive.
2. If at all possible, try the rifle on the range at 100-200 yds before buying OR buy it with a target which the rifle has shot at those ranges.
3. Don't try to make a sniper out of a rifle UNLESS it is uncannily accurate in your hands. A scope doesn't make the rifle any more accurate, it just makes the target look bigger.
4. Don't buy a sporterised rifle with the intention of putting it back to military spec UNTIL you have sourced the set of woodwork you need.
I'm sure others will have tips.
Rob