It all depends on your setup & self discipline. If they are let out of their coop first thing in the morning, every morning, without fail, and not put back in until sunset then food & water in just the run is fine. However, if you live in a hot climate, you should most certainly put at least water in the coop. I live in FL so I always have water in the coop. Also, if you don't necessarily let them out of the coop (that is if you close & secure it at night, like you should to keep out predators) first thing each morning, like if you sleep in or something, it's comforting to know they will have water.
I do not keep food in my coop though. It just makes a mess and can attract even more pests/predators.
As far as the water in the coop. I use an old milk jug with a $2 no-drip nipple waterer. I got it from TekSupply. It took them a while to figure it out, and a bit of training (poke it with a stick while they stand under it, lol) but they got it ok. In the mean time I had put their chick waterer in there just in case. They always managed to knock it over though and get all their bedding wet. So now that they have the jug it keeps it really nice and dry & clean in there. Minus all the poo of course. LOL. Oh, you can also use one of those rabbit/small animal waterers they hang on the cages.
I'm sure a lot of people have differing opinions on this, so this is just what I do. You'll figure out what works best.