When fitting a new made to measure bathroom cabinet in your bathroom, it is important that materials are used that can withstand moisture. A lot of steam is generated when the bathroom is used and that will condensate on whatever is in the bathroom including your new custom bathroom cabinets.
If you are after a painted finish I suggest using something like moisture resistant mdf. By using this type of material will ensure that the fitted bathroom cabinets will last a very long time.
When a wood finish is required, then your best option is to go for a solid wood. Wood veneers are generally glued to a non-moisture resistant core material (mdf or chipboard) and this can create problems with swelling if moisture gets to it.
Often laminates are used for built in bathroom furniture but over time moisture gets to the core material and it swells and later falls apart. It is therefore important to make sure the right materials are used for fitted bathroom cupboards.