Ok, I'll try to give you some stuff before my brain shuts down. Which might be quite soon. Again, go to the Technical whitepaper section, and there are lots of resources. You should steal from the best and invent the rest! (No really, stealing is good in this case

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Motors: Cardinal rule- don't smoke 'em.

This happens when you stall the motor(run current through it while the shaft cannot turn) and the ensuing high heat releases the "magic blue smoke" I'm sure you've heard of. Electric motors, which in the FIRST kit are all DC brush motors, like to run fast, but they produce the most torque at low RPM. Dilemma. You have to choose a "range of operation" that best suits your torque and RPM needs. Trouble with electric motors is, you can't easily have both. RPM and torque are inversely related in a DC electric motor. The bottom line is, if you can't get enough power in terms of compromising rpm or torque to improve the other, you have to either add another motor, or shift gears.
I feel that I have started to ramble, so lets try to start anew.
When you consider a motor for a specific job, look at its power curve. The specs from the 2005 KOP can be found in the "Tips and Guidelines" pdf on the FIRST website.(Be careful, the fisher price specs are wrong) The stall portion is important because thats where you stall the motor, and get the most torque. However, don't ever design a mechanism to the stall specs, because you'll burn the motor. Add a generous safety factor ( i.e.-I can move the tetra at only 1/2 the stall current) so you keep the motor happy. Thats where gearing comes in, and where you have to trade speed for torque, vice versa, or design another solution.
Rambling again, starting again.
General Characteristics of Kit Motors
CIM- Big black motor. We get a transmission with the kit bot for them, mainly used to drive robot. Second most powerful motor in kit (considering the old 12 volt FP) 4300 RPM free (this means with no real load, just spinning) and 64 oz/in at stall. (This is torque at the motor shaft. by reducing the speed of the motor output by gearing, you increase the torque. you don't normally need something spinning at 4300 RPM anyways.)
Fisher Price- Silver motor with black plastic gearbox. The 12 volt version is the most powerful motor in the kit. **Warning** BURNS EASILY!!!!! Be careful of the loads you apply to this motor, it will smoke! Used mainly for arms and manipulators, sometimes steering modules. The gearbox is sound, even as plastic, but don't cantilever it's output. This will result in poor performance or a broken gearbox.Don't remember all the specs. I only know the motor free speed with out the gearbox is 24000 RPM.
Window Motors(Nippon-Denso & Jideco)- The two black and silver motors with the funky looking gear looking output. They are different motors, but similar in characteristics. The silver motor is slighty more powerful. Used mainly for mechanisms, like arms, lifts etc. he motor is the rectangular thingy, and the silver thing on the end is a built in worm reduction. Hard to burn badly....
Globe-We got one of these in 2005. Its the cylindrical motor with a shaft coming out the end, maybe 8" long. Pretty strong, has been used in winches, arm drives, end effectors, steering modules, basically everything. We made an "industrial servo" out of one once. Less powerful than the windows. It's actually a motor with a planetary reduction built on already. These can be burned if stalled repeatedly. A bit better than the FP in this respect.
Van Door- Runs a van door! We got one in 2005. It's the black motor, with the cast worm reduction on the end, but bigger than the windows. It has a long metric output shaft. Lots of torque, like 75 RPM usually. Used for arms as well mainly, due to it's strength. More torque than the windows, but not really high wattage. (I make the distinction between wattage(power), and torque. Power stays constant through gearing, but torque is what available at the moment) Also hard to burn
Mabuchi- Ahhh....Don't know very much. Its small, fast, might be good for an end effector with the proper reduction.
That was long winded. Didn't I tell you??

Hope thats a point in the right direction. JVN, Paul Copioli, Andy Baker... the list goes on. And on. These are great people who will answer your questions in a more coherent manner than I. Good luck!
Wow. Interesting that this is my 306th post. ALRIGHT for #306!!!