A long time ago before I new better I purchased 2 cheap Craftsman knock off lathes. I soon found I didn't like using them much, they vibrated and flexed too much and I was always afraid I was going to loose my work. Fortunately the motors didn't last. After taking up space for a while I decided to beef them up and converted one into a mini lathe and the other into a dedicated small face turning lathe.
Both have 3/4 HP 3 speed motors one with 3 step pulleys and the other with 4 step pulleys. The bases are beefed up with channel, tube and angle iron, this makes them much more rigid and reduces vibration. For small stuff I now prefer the reworked mini-lathe over my big Rockwell/Delta.
The face plate lathe only has a 12" swing but its great for small face turnings. Low vibration and by loosening 1 bolt the whole machine rotates on axis for the most comfortable turning position. It is mounted on a 3/4" aluminum disk salvaged from a former employers scrap bin but a double 3/4" plywood lamination would also do.