If you plan on shooting in the big ground squirrel fields the 223 is going to be the most inexpensive to shoot. It'll do 300 yards in an accurate heavy bbl gun with a good scope. Ground squirrels are not hard to kill, just hard to hit at long ranges with out the proper equipment.
Years ago I started with a 22-250 and that is an excellent rig. I did the benchrest competition thing with a 222 and that also made a great ground squirrel rig out to that 300 plus mark.
The last few years I switched over to the 243 and in a Remington heavy bbl 700 VLS it made a dandy ground squirrel rig loaded with 55 grain Noslers at just under 4000 fps.
Several months ago I bought a CZ Varmit in 204 ruger. This was after I shot with several friends whom shoot the 204 for both coyotes and squirrels. This little medium weight barrel gun is rapidly getting to be my fovorite. It shoots as flat as the 22-250 with no recoil. You can watch your hits thru the scope, something that neither my heavy 243 or any 22-250 I owned would do.
Anyway bottom line is there are lots of good rifles out there. If your just going to shoot squirrels the heavy bbls will allow you to shoot longer between barrel cooling sessions. Most folks that shoot the big squirrel fields bring two guns and a portable bench rest.
My suggestion is to get into reloading if you plan on shooting more than a few hundred rounds a year. As for the gun, get one that you like the feel of. Caliber for a varmit gun isn't as important as most folks make out. Just remember .223 ammo is good and inexpensive compared to most other factory rounds. Try to get something under .243 caliber that goes above 3100 fps at the muzzle for a 300 yard plus gun. 17's, 20's, .224's and .243's all make good varmit rifles. Right now I'm really impressed with the 204 Ruger caliber.
My squirrel and coyote medicine
Rem 700 VLS, 26 inch heavy bbl in 243, 6 by 24 illumnated reticle mil dot scope.
Ruger #1B, 26 inch medium weight bbl, 243, 8 by 32 Tasco Target Dot scope.
CZ 537 Varmit, 25.5 inch medium bbl, 204 Ruger, another 8 by 32 Tasco Target Dot scope.
Just keep in mind that this varmit shooting is highly addictive and the one basic rule you must remember is you can never own enough guns.