The bed needs to be stiff and is usually made out of cast iron. A more mode approach is the use of granite, because it absorbs the vibrations and thus allows more precision. Working granite is pretty difficult and not really fun, so I'm trying something which is pretty close to granite: concrete.
There are a few approaches with concrete on the internet, which was used for provisory lathes during world war I , but they are all only theoretical and consist of CAD drawings.
The ways are CNC ways, which would probably allow the modification to a CNC lathe, but this is in the backlog right now.
Something which I'm a little sceptical right now about is the headstock, which only consist of two bearing blocks.