I would look into the Sauer 202 system.. a very nice setup in my opinion.
I'm running a 202 Classic in .300 win mag with S&B zenith in a 56mm objective in EAW detachable claw mounts and have to say, I'm growing very fond of it after the first season in the field.
As others have mentioned, swapping barrels is very easy and would allow you pick up another barrel on the same action size (maybe 6.5 swede and 30.06?). The cost of a barrel is (ballpark) 1/3 the cost of the rifle, so it's a nice option.
There is a downside though and that is weight.. my setup comes in at a portly 10lbs+.. Sauer does offer quite a few rifles with a synthetic stock though and in a standard action with a smaller scope should be a fair bit lighter.
Another rather annoying point, in my opinion, is that the freaking magazine only holds 2 rounds of 300 win.. it is a single stack design and feeds smooth as butter, but still. I picked up an extended mag (4 in the mag) but it obviously doesn't look as nice as a flush mag.
The upside of the weight is that the rifle shoots softly for a magnum, very comfortable, very well balanced, very accurate.
I was previously running a Sako Bavarian 85 with the same scope and optilocks in .300 wsm and unfortunately, I had the dreaded ejection issues (shell casings would ricochet off the bottom of my windage turret on the way out.. very bloody annoying when I noticed what had become a ding on my scope.. it is an issue for some people and there is not much in the way of a solution from the factory.
I miss the trigger on that Sako.. truly a work of art and better than the Sauer trigger in my opinion, which is still very good (single set, if that is your thing.. I don't use mine but some people absolutely love them).
You are in a good place and with your budget, whatever you go with will be a great setup I'm sure! Have fun