Mike here's the cartridges I'm presently shooting.
My go to the woods varmint rifle was the 22-250 for better than 30 years. About five years ago I switched over to the 243 mostly just for a change and the fact that I found a beautifully accurate Ruger #1.
For the last three years thats been my go to the woods calling gun. As my grand daughters have grown and hunted with me I gave my 13 year old my #1 last year for here deer and varmint gun. Now having to find a replacement I started shooting friends varmint rifles. I was so impressed by the new 204's inherent accuracy that I bought a new CZ 527 Varmint.
I have to admit that I've never owned a 17 Remington, but I've shot several and though I've never found it wanting I didn't jump on the bandwagon. I built guns and ran a small gunsmith business for 27 years and have to say the new 204 is a really impressive round. It shoots as flat as the 22-250 or swift with low enough recoil forces that you can watch your hits, or better yet your misses, thru the scope and carries enough energy that I can't tell any killing differences on coyotes between it and the 22-250 I carried for many years.
I shoot two different 243's a Ruger #1 and a Heavy barrel Remington VLS. The VLS makes a dandy long range rifle and is no slouch on coyotes at longer ranges. The 204 seems to kill as well out to 500 yards. If I were going to buy two different guns I'd go with the 204 and the 243.
Ruger #1 in 243.
Remington 700 VLS in 243.
And my favorite varmint rifle of all times the CZ 527 Varmint.
I don't think you'll go wrong with any of your choices and there's nothing like a beautiful piece of wood that surrounds a good hunk of metal that shoots well.