I have to clean soooo much because DH is disabled so I have got it down to an art. I don't clean like other people and quite frankly, I wouldn't advise anyone to! Good god. You'd have to be mad. I designed the entire house to control infection, though, so a lot of the work is done for me by fixtures and systems. But a few things that might translate:
Steam mop = essential! Steam mop all floors (we only have non-porous tiled floors everywhere) twice daily and it's so much quicker than double mopping. I had the light Morphy Richards one but that just died so I replaced it with a Vax, which is a lot heavier but the head is better for getting round furniture legs and you can get coral mops for it so, eh, I like it. The carers moan about this one though, because it is so bloody heavy.
Vac Mop = so useful. I've got one of those dust and vac things -Vax again - and use that three or four times a day to pick up dust. It's better than the hoover because it doesn't kick up any dust and it's really light and the mop heads can be sterilised in the washing machine.
Vienna broom = one of those brooms with big foofy sides that do the skirting boards as well as sweeping. Expensive but worth it IMO to save my back, and they last forever.
You can buy 36 packs of microfibre towels/cloths at Costco for £7.99 and 12 packs of tea towels for a tenner. I have one of those triple basket laundry sorters with the lift out bags, but then inside one I tie two redliners (infection control requirement) and sweep all the cloths and towels into that once a day. Ideally I'd have a cover for that bag but I have never found anything that will work properly - the carers just dump dirty stuff on top of the lid if it's closed, alas.
I put everything in the dishwasher. Everything.