Hey, Harley,
I posted a partial answer to this on the Gamo Gate, might want to check it out. If your CFX is stock, avoid heavy weight pellets, that would be anything over 9 gr. The stock spring uses thinner wire, heavies lead to accelerated spring fatigue and failure. According to Jim Maccari, a steady diet of heavy pellets needs a wire dia. of at least .128 as I recall. At the other end, stay away from the ultra light pellets, say under 7 gr. or so. They don't provide enough pressure build up to prevent the piston from slamming into the back of the chamber. Not a good thing. One thing to look for. Apparently Gamo sells the CFX with two different barrels. The "tight" barrel has the serial number on the barrel, the "loose" barrel has the serial number on the side of the receiver. From what I've read, the tight barrel shoots the heavies better, as well as the Crosman Premiers, but you should still plan on replaceing the spring. The other one DOES NOT like Crosmans, or Kodiaks. Like I said in the other post, JSB Exacts and RWS Superdomes seem to be best. Beeman Crow Magnums are also pretty good, but that's about it for my particular gun. And believe me, I've tried a lot of pellets! Oh, and my CFX hates anything in a pointed design. BTW, Beeman has over a dozen different pellets, the only way to find the one that works best in your gun is to experiment. Besides, that's 1/2 the fun. Don't know what your set up is for shooting, but the CFX is one of the few springers that prefers being rested on something other than the palm of your hand. Mine prefers a typical sandbag, with the fore arm rested just behind the balance point, and a fairly light hold. Hope this helps, and don't hesitate to ask for more info, or to clarify something. This is a good place for that.
Dave