in this case you've got to look a gift horse in the mouth to tell them no Encore i want three Handi's! and, you've got to buy scopes and rings for all 3....
i'd get the encore in 7mm-08 and learn to handload for it. it's a great caliber.
then, when i saved up, i'd buy the Handi' in a .204 cal'
with handloads the 7mm-08 is a Great deer, caribou, black bear, and elk caliber............and something of a varmint caliber, too. i'd make the most of the hobby by handloading is what i'm trying to say -- starting with that caliber. then later on the .204 gives you an Excellent varmint caliber as well. the 7mm-08 is varmint worthy....but strikes me as a big bullet for things like groundhogs and coyotes.
as a compromise: the .22-250 is a SUPER varmint caliber, and can do duty as a deer caliber if you don't do Texas HeartShots!
just my opinion,
ss'