Your questions asks for numerous possibilities.
Truly custom rifle
action, Nesika, Bat, Stolle, and a few others are out their but the Rem 700 is hard to beat for cost and ease of accurizing, winchesters are also good. A well accurized rem 700 action although not as robust as the other actions has proven itself through benchrest shooting and also long range shooting matches. It is one of the most popular actions out their and loads of upgrades are available.
Barrel makers, Keirger, Hart, Douglas, Shilen, Lilja, Pacnor, Broughton, Mike Rock, Black Star, Lothar Walther, a loads more all good barrel maker none are in any order of sorts just all great barrels.
Gunsmiths, Kirby, Chris, GA Precision, Jiff Hicks, loads of them out their pick one you'll not go wrong with any of them.
Some calibers would be any of the smaller in dia Allen Magnums as usually varmint means smaller bullet diameter, 257 STW, 7mm STW, 25-06, 6.5-284, 260 rem, the list could go on and on.
Not all of my suggestions would make everyones top three list but all of them will get you good shooting rifles capable of doing what your asking of it.