if you have to make your own cabinets, I would use laminated chipboard or laminated MDF. It has a hard plastic coating and is easy to keep clean. Ssome cheapo cabinets are coated with white or grained vinyl foil, which is rubbish.
You can get it from DIY sheds.
Needs no painting. After assembly you can run white bathroom sealant into the joints to hide any untidy cuts.
If you cut MDF at home you must use a mask and do it outside as the dust is harmful.
Some DIY sheds will cut it to the size of the pieces you need. this will give a smoother edge that if you cut it at home.
you can use dowelled joints or KD connectors
unless you are quite good at woodwork a home-made one will not be very strong or attractive so look to see if you can buy cabs on offer locally. Rigid-built ones ae generally stronger than if you screw them together, but of course are more difficult to transport.
the material is quite heavy.
If you want to put doors on it buy the doors first and design the cabinet to fit.
If you are making a floor-mounted one you can buy adjustable legs.
p.s. if you are fitting new worktops, take off the old ones and measure them carefully and get the supplier to cut it to size. If the old one is a bit loose/tight then try to get the new one a better fit. Beware, the walls of rooms are rarely perfectly straight and square. Unless you have a medium/large circular saw you will not make a clean cut. the hard plastic laminate will wear out your saw and make it blunt, but a TCT tipped saw can cope e.g. when cutting out for the sink.
p.p.s these are some wall cabs I made to fit ready-made unit doors. they are made of 15m laminated chipvoard 300mm deep. the DIY shed cut then to my dimensions and i used a dowelling jig. I am not very good at woodwork but these are reasonable. Once I had designed the measurements I made several.
