What age are the kids? It's only a toilet not a full bathroom so I don't see the need for tiling the full room. It is colder, you have to clean the grout round the sink area and I think it could feel quite clinical if you get it wrong. It's a small room, so I would go with a wipe-able paint or eggshell, a wall hung toilet if possible, a sink with large mirror stuck to wall to reflect light and then you can have any colour you like. I'd go for a neutral to keep it light and airy. With colour accents added with towels etc. As long as you can clean is easy then that's all that matters.

Sanitary ware. I'm having a crisis of decision making. I bought a new sink and vanity from IKEA: https://www.ikea.com/gb/en/products/washstands-taps/wash-stands/fullen-t%C3%A4lleviken-wash-basin-cabinet-white-spr-39891444/ However, it's occurred to me since that it'll take up too much of the room/floorspace, especially as the sink faces you as you walk in. I've been looking at other designs, and the wall-hung sink with a nicer-looking chrome waste could be a much better option. Added to this, if I'm tiling the floor, I'll probably need to buy a new loo, and IKEA doesn't do matching loos. Therefore...where can I buy a basic loo/basin package? What's the difference between a 'toilet and basin' and a 'cloakroom suite'? Should I go for one or two tap holes? Am I wasting my money? Should I just update the taps on the existing sink and tile-box in the waste?

I have an Ikea pull out bin that runs on rails that are mounted on the bottom of the cabinet. Works really well. Needs some careful measuring to see if it'll work for you. https://www.ikea.com/gb/en/p/hallbar-waste-sorting-solution-with-pull-out-light-grey-s79308803/

I like Wumi’s examples- particularly the second one! My own downstairs loo is very similar - I painted it in Dulux Breton Blue which is near identical to the picture. I also have a corner basin like you - I bought a corner mirrored cabinet to go above it, and because it’s frameless, it just blends in. My cabinet came from Ikea and looks to be no longer available. However this one is similar and not too expensive… https://bathroommountain.co.uk/madelyn-corner-stainless-steel-mirror-cabinet-600mm-tall