Plenty of sound advice, but there is one thing that hasn't been
mentioned. Modern motors are more compact than old motors, so you may
well be able to fit a more powerful motor than the original 3/4 hp.
There is a down side to doing this, though. Should anything go wrong
(say the tool sticks in the work, or you're tired and run the carriage
into the chuck, etc.) a more powerful motor is more likely to do major
damage to your workpiece and/or lathe. In this case you might be saved
by the belt drive slipping, but if so a larger motor is wasted.

Best wishes,

Chris