I've shot prairie dogs on three occasions. So, FWIW....
I took a 22-250 first time. Only shot it maybe five times total and put it away. Never took it back. Any dog within 500 yards goes down after the first few shots. Muzzle blast. Guys think it's because they've been shot over before. I know one of our towns hadn't been shot in three years.
My absolute favorite is my precision AR. If you miss, you have an immediate second shot. Of the four if us that went first year, I was the only one with an AR. Next trip three had them. Last time, all four.
There is a significant difference in muzzle blast from the 22-250 to the .223.
Anything bigger than a 22-250 is a waste IMO. I've honestly killed more the .22lr than any other round.
. We kill more with the .223, but the .22LR isn't far behind.
I also have a CZ in .204. If I didn't use the AR, it would be next. Shoots as flat or flatter than the 250 with zero recoil and way less muzzle blast. I am gonna try to get my CZ Hornet going so I can use it. I want something for the 100 to 200/250ish range depending on wind.
If the wind is up, I don't care what you use. Most time it's as much luck as skill at 400+ yards, at least in my case. Last time we were shooting a strongly varying direct cross wind. I was using my .204 One time you could hold just a few inches off. Next shot might get blown 6-10".
Anyway, if I were to take only one rifle, it would be my AR. If you want a bolt, it would probably be a 6BR. Relatively low noise, almost no recoil, and good to 1,000 yards with the right bullets. My S-I-L has a Savage that is exceptional. But it's a beast, not a carry around rifle.
Who needs a reason to buy a 17hmr?
the guys had two of these first trip. Wind pushes those little bullets all around. Didn't do a whole lot better than .22's.