The word "Composites" refers mostly to the fact that typical Carbon Fiber is a composite of the fabric and the binding/shaping agent i.e. the resin. You can indeed add the plywood or foam core or any number of other things to it, but at the basic level its just the fabric and the goo (that hardens through curing after a time) that makes it what it is.
Carbon Fiber has many many forms and uses, and can be laid up in many different and varied ways. The hard core money bag types use pre-pregnated Carbon (the resin is saturated into the fabric before hand) which is cut and laid into a mold and then put through an autoclave(a pressurized oven that insures all of the excess resin leaves the fabric) to cure. This is big dollar stuff (think Formula 1 and Racing Sail boats and such). That said, it gets much less spendy, going down in steps from there. The first one is actually a pretty big step, and is called Infusion (Vacuuming bagging where the resin is added in after the bag is under pressure, thus getting even coverage and only as much resin as needed). From there you go to normal Vacuum bagging, which involves laying up as normal and then putting your project in a bag under vacuum, which then sucks all the excess resin out. From there you get to normal layup, which involves just laying fabric into a mold and wetting it down with resin, which then catalyzes and hardens.
Carbon is inherantly more finnicky then straight fiberglass, because of its stiffness. This makes it harder to shape, more prone to having the weave come apart, and just over all a bigger pain in the ass. However, its certainly attainable for the average enthusiast.
I recommend having a look at
www.racingcomposites.net for a wealth of information about materials, usage and technique about using Carbon Fiber. It is mostly centered around cars and such, but its the same techniques no matter the use (apologies in advance for some of the "hey dude I want to cover my car in carbon fiber" ricey threads).
Honestly, a Carbon Kevlar blend would be your best bet at this, since the Kevlar adds impact resistance to the formula without adding weight. I"m pretty sure that there are pre fab tubing made of it too. That would let you get away from some of the more sticky and frustrating parts of working with composites.
Just know that working with composites is a frustrating and time consuming hobby, and it will take you a while to get it down, but the end outcome has a lot of potential for badassness. It'll be unique, customized and light weight. Think that strength to weight ratio compared to steel is like 10 to 1 at least. Food for thought for sure.
JH