You still didn't say how high is the lift and how fast. Synchronous motors work nicely at low RPM and medium torgue. They have 3 wires and a capacitor. One wire is common terminal and you apply HOT to one or the other side of the capacitor to get a change in direction. Speed is inherently constant.
How do you plan to drive this thing? Common mechanisms are "rack and pinion", "linear bearings, gear and chain, a linear actuator (usually way too expensive), hydraulic (very heavy loads), air cylinder, Pull from a drum.
The pain is usually the "linear bearings"
This is where "how far" comes in. Is it 10" or 10 feet?