.270 Win scope? .22-250? .223?

[Jack]

Assuming you'll use the 270 for open country hunting for deer, etc., I'd lean toward a 3-9 or a fixed 6x scope.
The 223 and 22-250... if you use them as varmint rifles for prairie dogs or rock chucks, power helps. I'd look at something in the 4-16 power range.
If you hunt coyotes with the 223 or 22-250, something like a 3-9 or 4-12 might be best.
There are a couple basic rules to be aware of. The higher power scope you buy, the more weight and bulk, and the smaller the field of view. That's why a 3-9 might be better for deer and coyote than a 4-16. The 3-9 is less bulky, and has a wider field of view at the low power setting. A wider field of view makes it easier to find the target quickly.
You can get a good scope, or a cheap scope.
If you want a good scope, buy something from Leupold, Burris, Nikon, Pentax, Zeiss' Conquest line, Weaver's Grand Slam line, or Bushnell's 3200 or 4200 series. All are quality products.
One more thing...objective lenses. That's the front lens. Some say bigger is better (they're wrong ). On a 3-9 power, a 40 MM objective is quite sufficient to gather all the light you can use during legal shooting hours.