Lots of custom rifles are built on Rem 700 actions. I'd guess it'd be a toss up between them and the thousands of rifles that have been built on Mauser 98 actions. The problem is that Remington doesn't sell just receivers. (Savage does with a .223 or WSM bolt head though. Limits your cartridge options.) A lot of people buy a 700 in the length for their chosen cartridge, just for the action.
Knew a guy, long ago, who bought a BNIB Win 70A, just for the action(I got the stock for $20Cdn and put it on my Cooey .243 M71. Glass bedded. Looks great. Shoots minute of deer. Consistently though.). He built a 17.5 pound .300 Magnum(used 190 grain match bullets) in a Douglas Premium SS barrel, 1,000 yard, target rifle for DCRA(same idea as NRA full bore) shooting. He won regularly too.
Mind you, there's 1,000 yard shooting and 1,000 yard shooting. Not all 1,000 yard matches are the same and most use different cartridges. Palma(800, 900 and 1,000 yards), for example, requires .308's using 155 grain bullets and nothing else. Other matches allow any rifle, any sight. Some are iron sights only(Palma matches are iron sights only). There's 1,000 yard Bench Rest shooting too.