re: Time to declare war on Squirrels. What kind of weapon should I get?

Deacon,
I'd suggest a 22 caliber air rifle. You'll want a heavy enough bullet to keep the load subsonic to minimize noise. Traditional thought has been, "22 for fur, 17 for feathers."

Gamo seems to be a solid choice. If it doesn't come w/ a scope and you decide to get one, do NOT get a rifle scope. Conventional rifle scopes won't last on an air rifle.

If you decide to go the route of a 22LR, I'd suggest using CCI's "Quiet 22." It's a 22LR round designed to be less noisy. It uses a 40 gr round nose bullet. It will not cycle the action of a semi-auto. Unlike shorts and CB longs, it feed from the rotary mag of a 10/22. In my 10/22's, it's much more accurate than 22 Shorts or CB Longs and is the most quiet 22 ammo I've shot.