Don't use the wall faucet variety, UNLESS you want to purchase a new top for the vanity. Or return the vanity. Pretty simple. The round hole was meant to have a faucet. Not a "cover" which may also allow water down under, which may also ruin the vanity as there will be no containing water lines beneath the little hole. Bad idea,

after watching my daughter and her husband agonize over the way their expensive timber floor has not held up well after 3 years, I would recommend tiles/wood look tiles with under heating. Their beautiful warm expensive floor looks like it always needs a clean and polish, not from neglect, they have cared for it well. One of the boards now has a slight and painful moan when it's stepped on :-( I grew up in a completely wood floor home and although it looked wonderful, my Mother hated it. ....and the mats ! Wood is a lot harder to maintain than tiles ,(no matter what the die hards say) the modern wood finishes are much better than they used to be.... But a piece of wood is rather arty no matter what it's used for and it does demand to be loved and cared for.....and if something goes wrong it's a lot more expensive to fix than sand and cement. Ultimately you have to be happy. BTW underheating tiles is warmer than timber :-)

Yes, I had noticed a lot of pics on Houzz, that's what gave me the idea! I certainly wouldn't put it IN the shower! We have a tiled shower, but the tiles only go as high as the glass surrounds, so there is about 30cm of painted wall above the shower, which is the part I was worried about with steam etc.

I love three in ones because if one bulb explodes, you've usually got a fair few backups before you have to completely fix the bulb (but that's just the laziness in me coming out). In my opinion, I don't think you need a demisting mirror because that's what the fan is for in the three in one.