Polyurethane glue is available in several different brands. Gorilla Glue is in our local hobby shop, ProBond is at the hardware store, pretty much the same stuff I think. Dribble out a small bead and spread it as thin as you can, roller works best for me.
http://www.lonestar-models.com/ for prices.
Thickness: I ordered 3/32" thick so I can sand without fear of sanding all the way through. If I were more careful I could use 1/16", but I'd rather work in my usual casual style and suffer the consequences. Master builder I am not. I think I ordered 100 sheets of 3" x 42" for considerably less than $100. That's more than I need, but I'll use it over the next few projects, then evaluate. If I could go to a store and weigh each sheet I would do that, but the local hobby shop sells the same stuff that comes in the kits.
It would be great if you could find a set or two of cheap foam cores and practice once or twice before doing your project. I learned that in art class years ago. (Our teacher would say, If you're not sure how it will work, and the whole class would join in: Make a model! She did not mean model airplane, but a throwaway before screwing up your masterpiece.)
CF substitutions for aluminum will help on wing tube and landing gear. On a plane this size I think titanium axles are worth the cost. On our grass fields I find the typical Dubro axles don't stand up well to even soft landings, and if you go to 1/4" for more strength they get very heavy, but the 3/16" titanium is light and stands up well. I believe they're a PSP product, available from Don's Hobby, Troy Built and others.