It only makes common sense to research something before investing time & money into it. You don't go & just point to a car & say "That's the one I want" ; or at least I *hope* you wouldn't. It's wise to figure out your needs & intended uses before you pick. I'm not going to try & tell you one's better than the other (pneumatic are better :-) That's your decision to make. I'll just try to help you make that decision. First you need to figure out your budget. Whether you choose combustion or pneumatic, you need to figure out how much time & money you'd like to invest into your gun. A decent combustion gun can be had for less than $50 bucks (USD) and 5 -> 6 hours max, where a pneumatic gun would cost close to $75 bucks on the low end and require just about as long to build (for a basic one).
Noise levels are also a consideration. Combustion guns create loud reports when fired. Pneumatic however do not. So if you are living in a somewhat urban area, a pneumatic cannon might be a wiser choice for you. However there are noise muffling devices, aka [silencers] out there that are available for purchase from other websites. Either way if you plan on using your gun regularly, keep in mind how much noise that you can ge away with making before someone calls the cops.
Another issue is fuels, I am a hard-core fan of propane in my combustion gun. After using Right Guard deoderant in my smaller gun, I grew tired of cleaning the chemical residue left inside after a number of shots. I also tried Right Guard in my 3" cannon & found that to get even a 1/2 way decent shot, that too much Right Guard was needed. So much so that after an extremely pathetic 30 yard shot, the excess Right Guard accumulated on the inside surface of the chamber & was actually still burning after the shot. So I switched to propane. I use a plain old [benzomatic torch tip] to mix the propane a little bit as it gets sprayed into the combustion chamber. Some stores might not sell propane bottles [XXX oz. type] to minors, however here in America/Ohio this has never been an issue (for me).
[cost per shot image]
If you're a minor & your parents already think you play with fire too much, pneumatic might be the way to go. Hell I'm 21 & I still on occasion catch hell for playing with fire from my mom. Another lesser issue is the reload cycle time; a combustion guns chamber must be vented of the used air & fresh introduced into the chamber before firing again. For most this isn't an issue, a spray gun hooked to an air compressor, a fan, a hair dryer, your lungs; all can be used to vent the chamber. Unless you've decided that a quick reload time is a must, this doesn't really affect your decision either way.
Then there's the issue of just how technical do you want to get. A combustion gun in its simplest form is easy to build, even more advanced combustion guns that rely on electronic ignition are still relatively easy to construct. The guns themselves aren't really all that complicated (IMO) to construct, it's troubleshooting them and getting them to work that can prove to be the most difficult part. You should keep in consider your abilities at reading technical drawings, following directions, working with shop tools. Depending on your abilities you should attempt to build a gun with an according level of difficulty.
A final consideration for either type of gun you decide to build is your handyman savvy: How well you know shop tools & your access to them as well. Although a collection of tools & such isn't necessary to build either kind of gun, you will at least need a drill & hack saw at the bare minimum. Even more fun tools are a sure benefit if you decide to build a piston or diaphragm pneumatic. Although added tools like a lathe, vise, & Dremel tool are not required they come in handy.
Next onto some Physics & Math.