I have bought a little plywood this year, and have a number of suggestions that might help.
I don't know what CDX is - never heard of it. However, a good exterior ply will be fine. The more laminates in the boards the better.
Shuttering ply (Eliottis, technically speaking) is shite, but a good material for making gussets and box beams for the framework. The boards for the face of your board should be half decent though, so don't bother with shuttering ply - it looks awful, and is full of filler, lumberjacks foreskins, dust, knots, etc.
Likewise, steer clear of any Chinese hardwood ply - although cheap it is super variable in quality (from poo, to utter poo!). I speak from bitter experience...
Hardwood ply from the far east is normally a bit better that the Chinese stuff, and not too expensive - a lot of walls are made of this. Check out some samples before you buy though. Quality varies massively from batch to batch.
Scandahoovian spruce ply is a reasonable choice (from a sustainable source, made of wood unlike the chinese shit) but quite soft. Lightweight and easy to work with though.
Birch ply is the stuff, but super pricey. Given the choice, this stuff will make a wall that will double as a bomb shelter for us all to hide behind if nuclear war breaks out!
Above all, go visit your local timber merchant and haggle. If you let them know you need a load and let them know what its for, they should be able to style you. You should be paying between £15 a sheet (for good eliottis, if there is such a thing) and £25 for a good stuff. Birch ply will be probably be £40 a sheet, but it is worth it if you're going big!
Or finally the option for the board builder for whom money is no object - inch thick birch ply.Our campus board is made from it - it was so heavy it took 2 of us just to lift one sheet, but is awesome stuff. A must for the super rich wood fetishists out there........they do exist....