I strongly recommend that you build the coop before you get the chicks.
Then you can brood them right in the coop, and there is no question about how soon the coop will be ready.
It also saves the bother and cost of setting up a separate brooder area.
Definitely a good reason to build the coop before getting chicks.
If anything comes up to prevent you building it, you can just let it wait until you are able to work on it again, and wait a bit longer before actually getting the chicks.
No firsthand experience, and they may have different packages in different parts of the country.
Many starter packages include extra things you do not need.
Needed things:
--heat source (heat lamp or brooder plate).
--something to hold food and something to hold water.
Think about what feeder and waterer you want to use when the chickens are grown up. Some styles can be used by baby chicks from the first day, so don't buy special ones for chicks until you know if you will even need them.
Things I have seen in starter kits that you probably do not need:
--a roll of cardboard to surround the chicks (only useful if you are brooding chicks on the floor of a big, safe building. Even then, you can use a big box, or cut pieces from boxes and fasten them together.)
--thermometer (if you already own a thermometer, just use the one you have.)
--little bag of chick feed (just buy the big bag, which is much cheaper per pound)
--booklet on raising chicks (you have the internet, and libraries often have good books too)
I'm pretty sure I've seen other not-needed things in such kits as well, but those are some of the most common ones.
If you need some items that are in the kit, and if the kit is genuinely cheaper than buying those items separately, then it does make sense to buy the kit. I just haven't seen a case when that would be true for me.
Check your zoning, and if you have an HOA or any restrictive covenants on your property you should check them too.
Some areas permit chickens, many suburban areas forbid chickens, and some make you get a permit or comply with special rules.
I'm sure you do not want to build a coop and get chicks, and then learn that you cannot have them, or learn that the coop should have been 10 feet further from the property line, or that you are only allowed to have 4 hens, or something else of the sort.
Setbacks from property lines, and limits on how many chickens, are pretty common in suburban areas that do allow chickens, but the exact numbers vary from one place to another. So you definitely need to check the rules in YOUR area.
Shade and ventilation are very helpful in hot weather.
I suggest you NOT build the style of coop that looks like a solid little house with an attached run. That style is good in cold climates, where the chickens spend long stretches of time indoors, and only use the run in good weather. (Common size advice: 4 square feet of space per chicken in the coop, 10 square feet per chicken in the run. More space is always fine.)
If you want it to stay in one place, I suggest you build an open air coop: solid roof, wire mesh for most walls, just enough solid walls to keep wind & rain off the roosting and nesting areas. Allow at least 10 square feet per chicken, because this serves as both coop and run (of course it is fine to attach an extra run as well.)
Or you could choose to build a movable coop (sometimes called a "chicken tractor")
Moveable coops often use wire mesh to keep predators out, and tarp instead of solid material on the roof and walls to keep out the weather. Plan on securing the tarp so it doesn't blow around, and replacing it every year or so.
Since you also want to garden, it could be nice to put the chickens in one place for a year or so (kill weeds, fertilize the soil, make compost in the chicken pen). Then move their pen over a few feet and let them prepare another place while you grow plants on the first spot. Over several years' time, you could rotate them around however many sections of garden you want to have. If you only move it once or twice a year, it doesn't have to be quite as light and portable as the ones that get moved daily. Just make sure it is not impossible to move.