I like a sporter weight barrel for walking varmint hunts here in the East. A .22-250 will be a bit warm in about 5 rounds, but unless shooting prarie dogs, that shouldn't be a problem. I had a Rem Varmint special that I had to get rid of because it was just to heavy to lug around the chuck fields, and I was a strong 20- something at the time.
My standard weight, 24" barreled, .22-250, Remington 700 ADL, built in the 80's, is a fantastic rifle. The Rem light varmint rifle might be the one I'd choose today. I just like the way Remington stocks fit me and like the pistol grip/trigger configuration.
If there were a 24" barreled Tikka or Sako in .22-250, they would also be nice, but maybe a bit light with the plastic stock, I'd probably choose wood.
The CZ varmint model I looked at weighed way too much for my tastes as a walking rifle.