I'm only picky about 3 things when it comes to strings:
-Gauge. This is obvious I guess. Who wouldn't?
-Material. Nickel or Nickel wound, no Steel strings for me. They sound too harsh and eat frets alive. I mostly use Nickel wounds, and will try some pure Nickels soon. Pure nickels are a bit easier to play too, aren't they?
-Strings
not being Fender. I don't care about brands mostly, but Fender strings have always been horrible to me for some reason so I steer away from them. I usually end up with D'Addarios because they're cheap and reliable.