As an old hack at amateur robotics and other things electromechanical, forget the threaded rod for a jack screw unless your load is light. They will gaul up in no time when put under moderate loads. Yeah, you can find super smooth ones made for motion control, but they will cost more than non precision acme lead screws. Go find non precision acme lead screws, or use a different type of drive mechanism. Think carefully about your drive mechanism and how it will or won't intrude into the interior, and other spaces.
On acme threaded lead screws. You may be able to scavenge them out of old hospital beds, or other equipment. A big issue will be getting ones long enough. You might have to design leverage into your system. Hum, non precision 6' and 12' ones are now available at McMaster-Carr:
http://www.mcmaster.com/#general-purpos ... ds/=lgtx9i so I guess length won't be an issue. Plain steel ones are cheap enough to ignore threaded rod. I wish they handled them a couple decades ago.
A cordless drill will be powerful enough. If needed it is easy to gear it down some with a simple chain drive. Look on craigs list for a 12V or 14.4V drills with dead batteries. Hook it to your house battery with some stout wires. Use a high current relay to control the power it. Those drills can suck down the amps when loaded. Note, some higher end battery operated drills already have gear boxes in them for higher torque output.
Ball screws have an advantage in the turning load pressure is across ball bearings, and thus are easier to turn. They have the disadvantage of not have that great deal of friction to resist being pushed so a brake of some sort is needed. You could use a magnetic brake. There are ones where you provide power to release the braking force. In the past I've found them at electronics salvage places. If you scavenge a ball screw, don't remove the ball nut from the lead screw unless you like the nightmare of reinstalling a large number of ball bearings into it again.