- Do I need a motor driver board since the motor works best at 12V?
- Is there an alternative to driver boards?
- How do I power the motor?
Yes, you probably want a motor driver board. You can pick up an L298N board on Ebay for about $5, and that should work.
There is probably an alternative. If nothing else a DIY motor driver board would count as an "alternative" but I don't know enough to make a good recommendation. I do know that you definitely can't just connect the stepper motor to the GPIO pins and have that succeed.
You can power the motor with any 12v power supply. I would recommend a 12v wall wart, such as one you might find with a laptop, printer, or network equipment. I don't know if it would be best to run the motor wires the distance between the Pi and the motor, or if it would be better to mount the driver board next to the motor and run the GPIO lines and power the longer distance. I suspect the latter, but I don't know, and it may not really matter. Either way, since your Pi is on the floor and the motor is on the ceiling, you'll definitely need several wires running up the wall connecting the two. (If it was me, I'd probably use an Ethernet jack at each end and run a standard 4-pair Ethernet cable between the two for your connection, just to keep it tidy, rather than running alarm wire up the wall.)