Saw a cougar last year outside my place. Got my firearms license (there is such a thing here, requiring written and practical safety exams) around the same time, along with my hunting license (requiring another written exam), but still haven't bought a gun.
I'm thinking a Remington 7XX .308, and, on advice from others on this site, spending at least as much again on decent glass.
My dad got both of his licenses the same time as I did - and in fact wouldn't have passed the hunting exam without me whispering answers to him (not really being able to retain the difference between a cartridge vs a shell, much less diving ducks vs puddle ducks, or woodcock vs ruffed grouse), and having checked out some shotguns a few weeks ago we both really liked the feel of the Mossberg 535. He plans on getting one as soon as Bass Pro gets the gun safe he wants in stock... I'll probably wait until I've got the rifle stuff and some other outdoor gear first, though.