Noob looking for little advice...

[magicniner]

Which confuses me as my digital readout on the lathe is X and Y. There again, the lathe functions perfectly well without a Z axis (do I hear a violin plaintively playing 'Hearts and Flowers'?)

That just means it's a generic 2 Axis readout that is not specifically made for a lathe and is thus incorrectly labelled for lathe use.
If it were a Lathe Specific model it would have lathe specific functions including Diameter and Radius display of X and a table of offsets for tools/holders, like this one-



That's my 0.75Kw, 20 year old Siemens Micromaster Vector on the left BTW ;-)