I'd get a Remington or Savage action, or large-ring Mauser, then have a good barrel made, and add a good stock. Your barrel-maker will help you on the specs for your goals, but you want a 1 in 7.5 or 1 in 8" twist rate in the bbl (maybe even tighter) if you're going long range, to stabilize the very-heavies (160/162s). Like the man says, these days, a used Savage action (rifle) is less than a Mauser other platform in some cases. But not usually.
You could also just run with a factory Sako, Tikka, Howa, Winchester, or CZ chambered in 6.5x55, and it *may* shoot just as well as you want it to, without tinkering or new barrel, or only a minimal amount of tinkering, like glass bedding and/or pillar bedding. Maybe Steyr has one too.
Ask our resident flamboyant troll (JK
) WildAlaska about his Blaser rifle with custom 6.5x55 barrel - apparently it shoots itty bitty 1-hole groups. Expensive though.
DSA Arms will make you an FAL in .260 rem, which is approx. equiv. to the 6.5x55. You can also get AR10-type rifles in .260 rem - I want to say G.A. Precision will make you an upper in .260 rem, but I may be smoking dope. But you're better off NOT building a semi-auto, if you want to see what the round can do, so that you can load them long and hot. Turnbolt is the way to go, for safety & extraction reasons; and feeding reasons as well.