twirap:
Also, I have access to university student machine shop so I can use that.
If you go the route of using the machine shop, please, for the love of mike, take a class on using the machine shop (if the shop is smart, they will -require- this). Machine shops, machines, and tooling is not something you "play" with. You can't just go in and expect to easily figure it out. It can be dangerous; you need to understand and respect what you are doing. One slip-up, and you can lose a finger or worse.
twirap:
I should probably get me a thick sheet of aluminum and stick the gear on there and pin a needle or such through it to keep it in place.
You probably don't really need that thick of aluminum; you could even build your gearbox with acrylic or other lightweight plastic (like sheet styrene or sheet ABS). Have you ever taken apart a cheap toy with a sheet metal gearbox (maybe they don't make 'em that way today much; probably all molded plastic nowadays). Anyhow, thick aluminum is not needed, unless you expect to put a lot of strain on your gears (and if the gears are plastic, they'll fail long before the frame of the gearbox).
Your idea, though, to prototype the gearbox is a good one, though - especially if your gears are "random ad-hoc" piece where you don't know important things like pitch-circle sizes and whatnot...
So - get some cardboard, or sheet styrofoam, or even foam-core board; use wood dowels the size of the shafting for the gears, and poke the dowels into the board where you need the gears. Use pieces of cardboard, etc to act as "spacers" if you need to "stack" the gears. You might want to rough out placement and such on some graph-paper first (or paste graph-paper over the top of the prototyping substrate you are using - you might even consider printing something like this up, at a known DPI spacing, for later measurement purposes). You want your gears to mesh tightly, but not so tight that they will bind, and not so loose that they will slip under stress, which will just wear the teeth. Mounting the motor with it's pinion gear will be trickier, but doable (maybe a drop of ink or something on the end of the shaft, and press it on the paper to make a mark?)...
Once you have your prototype laid out, you can transfer the measurements/positions to another template paper or something, or scan it in at a known DPI and clean it up to a template to paste onto your sheet metal. Then mark the locations for shaft holes and such on the sheet metal with scribes/punches, then use a drill press or such to drill it out for the shafts (make sure you clamp the metal when doing this - DO NOT TRY TO HOLD IT WITH YOUR HANDS). Mount the shafts with solder (steel or brass shafting only) or epoxy. Or, if the shafting it long enough, use a die to cut threads and mount using nuts on either side.
That's the real basics. This isn't to say it will be easy, or it will work correctly the first time out. If this is your first time doing anything like this, it will probably be better if you looked for an off-the-shelf gearmotor solution first.