I look for consistency. In 3, 5, 10-shot groups, whatever I'm doing. I want to duplicate results and prove the load near and far.

At 100 yards:
<=1" groups for medium/big game rifles

<=5/8" groups for varmint rifles

Less is always better but if I could achieve the above results with a rifle I really liked, it would be sufficient for my use. Anything larger or signs of inconsistent performance in a modern bolt action rifle and it would be sent down the road regardless of how much I liked the rig.

Also, I usually have an idea of what the rifle will do in pretty short order. After confirming the rifle is properly assembled(so there is nothing mechanical that will hamper results) I won't dick around shooting 100+ rounds for load work up to make my decision. If a given rifle is that fussy from the get-go, I don't want it.