People do it both ways for different reasons. Some of the things I suggest you consider.
If you leave them locked up in the coop in the morning for a petty good time after they wake up, they need food and water in the coop. If you do not sleep in on weekends, that may not be a consideration.
If you feed and water in the coop, they spend more time in the coop. They poop a lot. You might need to manage the poop in the coop more. But, if you have a fairly small run, you may have to manage the poop out there also. You may find it easier to manage the poop in the coop. I don't know. It depends on how you are set up and your management practices.
Feeding in the coop will attract rodents. Feeding in the run will attract rodents. I pretty much find this is a wash, but it is a big deal to some people. I don't try to keep rodents out. I try to manage the numbers.
They are going to spill water. Having water in the coop may give you a wet coop, but I don't have that problem. Again, it depends on how you are set up.
Many people find that when feeding outside, they wind up feeding a lot of the food to wild birds.
Chickens are going to spill food. I have bedding in my coop but my run is dirt. Mine find more of the spilled food in the run, so I have less waste from that by feeding in the run. However, read the wild bird comment.
The feed needs to be kept dry. From your description, it sounds like you can manage that whether inside or out.
In your climate, it is probably not a consideration, but in some climates there are days that the chickens cannot go outside to eat or drink. Some people have to heat water or be around to change it out a few times a day. Lots of different ways to approach this.
I'm pretty confident others will come on with other considerations. There is no right way or wrong way, just the way that suits your particular situation the best. Good luck and welcome to the adventure.
