Personally I would board over the existing floor, taking it up on an old house might uncover more problems than you want to find! If your struggling for height you can always use NoMorePly as its fully waterproof and only 7mm thick, the board needs to be primed, glued and screwed before using a decent flexi adhesive to allow for movement.
As Dock says you need to get the bath plumbed in, sort out all your pipework, boxing in etc before starting on the walls. Once the walls are done finish by tiling the floor.
Skysurfer, if you do one thing make sure you get your settng out right, if you get it wrong it could cause you no end of problems!
Best of luck,
cjbombero