This! . @Marbles nailed it. Lived and hunted in Idaho my whole life. Everything from moose to antelope including varmints. That 243 will do the job. No need for a magnum. I suggest using that cash to get very confident In your current rifle especially if your planning shots at a decent range. Let me tell you the weather/wind out west can be unpredictable and shooting 600 yards is not the same as a flat range.Best budget rifle is the 243 you already have. I use a 243 and 223 and live and hunt in Alaska. So long as it meets the arbitrary legal requirements of were you are hunting, there is no sub $650 rifle I would recommend.
Well, if you can find a deal on a fast twist 243 Tikka and reload to take advantage of 108 ELD-Ms or 103 ELD-Xs, that would be it.
If you don't reload, and don't feel comfortable with a 243, the find a deal on a 6.5 creed Tikka.
If you must buy a new rifle I would spread out your caliber selection a little bit and go 6.5 Creedmoor. Cheap, can buy ammo anywhere and will easily take anything out west as well. Like others have said with the tikka rebate I'd definitely pick one of those up if the budget was $650ish.