
Welocme to the forum!

Glad you joined us!
You don’t understand how hard your question is to give a really good answer. We keep chickens in so many different circumstances, in so many different climates, with different flock make-ups, for different goals, urban or rural, and using so many different management techniques that there is no simple answer that really fits all of us. Add to that a whole lot of things we discuss are really only important to people. In a whole lot of cases, the chickens don’t care nearly as much as the people.
The easy answer is that cats hardly ever bother grown chickens. They are a risk to young chicks.
It sounds like you might live in suburbia. Have you checked local laws to see if you can legally keep chickens?
Your climate will make a big difference in what kind of coop you need. In the southern USA, cold is not your problem, heat is. Even pretty far north cold is not really as much of a problem as a lot of people think. With their down coats, they can handle cold pretty well, but they do need some protection.
Chickens are not all that hard to keep from a chicken’s perspective. They need feed, water, some protection from the environment and protection from predators. Especially if you are in suburbia, noise and smell might be issues. As long as you keep the coop and run dry, the smell probably won’t be bad at all. But it is real hard to keep a run totally dry when rainy weather sets in. Some members of this forum that live in suburbia work kind of hard to manage that. I’m in the country. That’s not an issue for me, though a wet run can be a dangerous disease ridden run so I do pay attention to it. I just don’t work as hard with it as some people do.
With them that close to your house, the smell and noise might be a problem. They create a lot of dust too, both from shedding dander and scratching. They create a lot of poop. You may wind up managing that. I compost mine for the garden. I don’t know if that is an option for you.
I don’t know what that deck is like. Chickens can fly and just jump up pretty high. Your problem may not be under the deck but on top.
I don’t know what your fence looks like. I’ve had chickens get out of a 5’ high fence. Some people keep them pretty well contained in a 3’ high fence. Whether they want to get out or not depends on their motivation. Some individuals just like to roam.
A coop does not have to be that expensive. Like I said, the chickens don’t care. A coop needs a roost. That’s dead simple. A tree limb or 2x4 works fine.
You need nests. I’d suggest two for what you plan. We do a tremendous amount of different things for nests. Some really simple and some people build some really complicated things. If you want a cheap nest, go to a local bakery or deli and get an empty 4 to 5 gallon bucket. They usually give them away for free. Figure out how to put that about a foot off the ground and at a 45 degree angle. Pot some hay, straw, or dried grass clippings in there. A perfect nest.
They need a way to get from the coop to the run. Make that as simple or complex as you wish.
You need access to the coop to gather eggs, take care of the chickens, or maybe clean. That’s probably the most complicated part of the whole thing. Whether that is a door you can walk in if the coop is tall enough or something you can raise, slide, or swing if the coop is smaller.
You need good ventilation, no matter where you are. I get that by having openings under the overhang so it is over their heads when they are sleeping. In warmer climates you still need openings over their heads but it doesn’t matter so much about the breeze hitting them.
You need to keep the feed dry. That may be in the coop, under the deck or somewhere else.
There are so many ways to do any of this I can’t get very specific.
Good luck!