Welcome to the Bunnings Workshop community @Jeanie7. It's fantastic to have you join us and many thanks for your question.
Please be advised that due to the vintage of the property there is a high likely-hood that the paint is lead-based and the walls constructed from Asbestos sheeting. Due to this, I would recommend you only clean and paint the surfaces and do not disturb them with sanding at all. This is in line with Government health and safety guidelines on Asbestos.
Would you be looking to freshen up this bathroom or complete a full renovation? It might assist our helpful members in giving some great advice if you could provide a little more detail on what you would like to achieve.
To refresh this bathroom I would advise starting by using a stiff bristle scrubbing brush and sugar soap to clean all surfaces within the room. You will then need to rinse off the sugar soap with freshwater and allow to dry.
Use Rust-oleum Zinsser 3.78L Bulls Eye Primer Undercoat Sealer And Stain Blocker to prime all the walls in the bathroom. You can then select a suitable bathroom paint similar to Dulux Wash&Wear Plus Kitchen & Bathroom Semi-Gloss Paint. I would suggest going for at least a semi-gloss level of sheen as it will prevent mould and mildew build-up and be water resistance in the shower recess. Please be advised that the use of paints in a shower recess limits their lifespan dramatically. You could look at painting the shower walls with oil-based paint or investigate epoxy paint options.
You can paint your window trim with Dulux Aquanamel for a hard-wearing finish.
The tub and basin look to be in reasonable condition and still functional. If you wished to paint them you could use Rust-oleum Tub And Tile Refinishing Kit. Changing the colour to white will certainly update their appearance.
We look forward to hearing additional details about your project and assisting with some solutions.