Use a stepper and a gearbox 1:6. Using a stepper nema 23 with 200 steps per turn, you will end up with a system with 1200 steps per turn or your gearbox shaft with a torque 6 times higher. You don't need special gearbox, since your system will pull always in the same direction so no problem with the possible backlash.
Using a stepper you have much more control on the system. If you will need a close loop system, then you can use an optical encoder driven directly by the wire, this will increase the precision of your feed, because in case of possible slip (your wheel driving the wire is acting on friction and slipping could occur) the close loop could easily compensate such an event.

Alberto