Your choice of motors depends on two factors: Speed and cost. Powerful (=fast_ motors are more expensive than less powerful (=slower) motors. CIMs are what I'd call "expensive" and the Denso window lifter motors can be had for much less.
CD drive motors are not a bad option.
I always keep my eyes open for sources of motors. On trash day look for things that might be useful. Most appliances have AC motors, not useful, but treadmills have large, powerful DC motors free for the taking. If you live in an area where they have cars, look for a salvage yard (aka Junkyard) - you can buy window motors for $5 each or less, maybe even free if you explain nicely what you're doing with them (the 'poor high school student building a robot' routine works well). Just learn how to get the door panels off a car, as they'd like for them to be in sellable condition when you leave...
You asked of the cold cathodes would kill your battery? Not much, they are not very power-hungry. Once you connect one, measure the current (you do have a multimeter, right? If not Harbor Freight sells then for $3)