How much are you willing to spend?
"...choose motors that don't use spur gears. In a high-torque situation, it is very easy to break the teeth off the gears, and destroy the gearbox (which may or may not be easy to repair - or if so, may or may not be inexpensive!). ..."
Yes, I was worried about this. What are the typical specs for torque on gears?
"...it might be cheaper to purchase a linear actuator)....
I don't know what it is, but I'll look for one.
"...if you can find it, go for a gear motor that uses a worm gear to a spur gear (a windshield wiper motor or a window actuator motor from a car are low cost examples).
In fact, I thought of a spur gear and worm gear, but the teeth may break, and the shaft is raked back from the vertical so the worm gear on the chassis and the worm gear on the motor will not be in-line.
For my situation (which I am still working on), I ended up building a homebrew linear actuator mechanism using a 7.2 VDC cordless drill motor/gearbox with a piece of all-thread as my lead screw. A couple of nuts with a bolt JB-Welded to it form the travelling nut (if the JB-Weld breaks, then I'll try a real weld job instead). It should be a cheap (the drill I got at Goodwill for a couple of bucks; the rest I spent less than 10 bucks on) but powerful form of a linear actuator, as well as having much faster movement than a standard linear actuator (1-2 inches per second seems reasonably possible from my testing).
I have such a drill motor and I have yet to check the gears, but again - how to mount them?