IMO, action choice is not just the action, but trigger and bottom metal too.
Tikka has a pretty true action. That is almost custom level. Many folks don't true them and there are even some prefits available. The trigger is pretty close stock and there are a couple aftermarket available.
Remington 700 should be true'd. Actually, I'm not sure who would fit a barrel without. The extractor is suspect, but serviceable. The ejector is inconvenient. The action is rough. The actions are often out of time.
Winchester 70....generally great extraction and ejection. Safety is good design and execution. Action needs true'd or at least checked for true. Decent trigger and bottom metal choices.
Howa 1500 ....basically an improved Rem 700. Not sure on accuracy. Some trigger choice and bottom metal choice(I think)
.....or, you really need to consider a Bighorn action at $800-$900....rem 700 pattern, but a truly custom action.