Some questions: How much better is 1" wire than 2", and how much more expensive? How airtight does the coop need to be? How much outside yard space is needed for just a few chickens for eggs? And, what is the easiest and best way to make nesting boxes?
First, there is a big difference between chicken wire and hardware mesh "cloth" (deceptive name, as it is metal). Chicken wire is designed to confine chickens, NOT keep out predators. For this reason, many chicken keepers eventually switch to the mesh (typically 1/2 inch grid). Hardware cloth is more expensive, but chicken wire will just be breached. Predators include: predatory birds, snakes, and roaming cats and dogs in most areas.
Going from above, I try not to have more than a 1/2 open space anywhere in the perimeter of the coop. Anything bigger, and a snake could easily get in. (one big enough to do damage).
As for space, I have a 16' long, 6' wide, 6' high coop for my 7 chickens, and they seem fine with it. I'll actually be adding a chicken run to it eventually this year, just to give a bit more space. Note, you also want the walls of your coop to go into the ground, at least 6 inches deep, though a foot is more recommended. This will guard against digging predators (like racoons, etc.)
For our nesting boxes, we just have a long wooden box, divided in 6 different openings, each about 12 inches by 12 inches, by 12 inches. There are lots of options though here, to use what you have (such as milk crates, old buckets, etc.)
The bigger challenge has been best solutions for feeding and water. For feeding, we eventually made PVC tubes, that have a 45 degree elbow at the base, as a gravity feeder. For water, we opted for the larger, plastic water inverted jug (I think it is about 5 gallons), that has a little trough around it. (the nipple waterers always clogged, etc.). As a tip, keep the water jug raised from the ground some (to keep them from getting the trough all nasty with dirt, etc.).
We keep 7 chickens, and generally always have about 4 dozen eggs in the fridge, at any given time. Fun fact though, eggs will actually keep a while before you need to refrigerate, we just do it more out of habit.
The nice thing about keeping them in a coop, they are protected, and it is easy to collect eggs. With free roaming, you'll always lose some to predators, and you'll likely never find all the eggs in a given day (which is usually fine though, because as I said, they do keep)...but of course, lots of other animals may find the eggs and eat them too!
We're in FL here, so gets hot, so for that reason, we have a fan mounted to blow into the coop. Likewise, we have some nails sticking out along the roof, that correspond to grommet holes in a long tarp. We put up the tarp if we're getting a really bad rainstorm or a lot of wind on a particularly cold day (though cold days are rare). You'll want to consider any environmental factors (heat, cold, rain, snow, etc.) and their impact to your birds.
All of the work is really in the setup. Once going, maintenance is pretty easy. Unless you want breeding, be sure to get only "Pullets" (hens) when you get your chickens, but beware, the guys at the local feed store etc. can't always tell, so you may end up with a rooster in the bunch. Best if you learn to tell yourself too...just to confirm. Don't get any runts (because they are cute). They likely won't make it...sad to say. There's different feed for chicks, but a few months in, you can then switch to layer crumbles. At least here, Walmart sells it cheaper than the feed stores, and I've had no problem with the feed there.
One thing we like: decoy eggs. These are ceramic eggs that look and feel just like the real thing. They do two things. One, if a snake gets in, could choke itself on them. Two, encourages the hens to lay in their boxes. We dot each decoy with a marker dot, to tell it from the real eggs.
