A water dish is fine. A lot of rabbits seem to actually prefer dishes to bottles. Changing the water once a day should be fine unless the rabbit gets the water really dirty or spills it.
The wire can hurt their feet, I usually advice trying to make or find a cage without a wire bottom. I have a dog crate (for my dog) with a pull out tray and it doesn't have wire that goes on top of the tray.
Shredded newspaper should be safe but it's not very absorbent and you may have to change it often. Are you planning on litter box training the rabbit? If you are then I'd only put litter in the litter box.
Maybe you can find something else to cover the wire. Foam pads? Maybe something like this, cut to size. I know quite a few people who use these for rabbits...
Or maybe fleece blankets folded up so they make a thick barrier above the wire?
Is there any way you can remove the wire? If you litter train your rabbit then you won't really need the wire there to keep the cage cleaner.