"...want one gun to..." It's not always about wanting just one firearm. Not everybody can afford more than one. A shooter who owns one rifle tends to be extremely deadly with it too.
Yes, a .308 with a change of ammo will kill any game you care you hunt. Think 165 grain hunting bullets for deer/bear/moose, etc and 130's for coyotes. Mind you, there's no reason not to use the 165's for Wiley too. Unless you want the hides. You will have to try a box of as many brands as you can to find the ammo your new rifle shoots the most accurately.
Factory ammo isn't cheap though. Get expensive quickly. Runs $16.99 and up, depending on where you buy and what brand. Reloading makes a difference. A Lee-Loader Classic with a scale will do nicely for an new shooter on a budget. They're slow, but will produce good ammo.
Hi, sureshot. If you want a new rifle, look into a Savage Model 10 GLXP3 package(comes with a low end, but serviceable scope), if you want a wood stock. A Model 11 FLYXP3, if you want a synthetic stock. Same rifle with a different stock. Change the scope when your budget allows.
Don't discount buying a used rifle though. It's not like buying a used car. It takes a great deal of abuse to damage a modern commercial hunting rifle. You'll likely be able to find a good used rifle with a scope in your local gun shop.
"...how do you get a quote..." Click on 'User CP', then Edit Signature under 'Settings and Options'. Type in what you want and save it.