...RSAUM, roughly in that order of preference. Hon mentions to 6.5 Creedmoor, .270 WSM, 6mm Rem, 6.5-.284 Norma, and yeah, .308 win.
.308 isn't a *bad* choice by any means, but it wouldn't make my top ten. I might even put .243 first for your purpose...love that chambering for deer...