There are many ways to raise chickens successfully. I would encourage you to do some reading in our learning center and coop section, as well as predators and pests.
That is a rather expensive brooder setup, and it looks like it will quickly be insufficient for 25 birds. If they stay under a heat lamp for 4 weeks, it should be about 1 sq ft per bird, so 25 sq ft, and larger if they stay under longer. Depending on your setup, they can be outdoors from the beginning, if you have it set up where they will be warm enough. 25 chicks will produce a huge amount of dust and dander, and will smell at least part of the time. A garage or covered porch, or even the coop if it is ready, can be used to brood them, with power. They are supposed to need 90 to 95 degrees F for a week, then reduce this each week -- but they will also need room to escape the heat if they wish, and you will probably find they want the heat reduced faster than this. They are "officially" ready for outdoor weather when fully feathered at 6 to 8 weeks, but again, many old timers put them in the coop much earlier, maybe at 3 weeks, if they aren't there already. Some will want to be warmer than others. You can build a simple box for a brooder, which will need some sort of open air top like wire screen in a few days or they will jump and fly out. Or you can simply brood them in the coop, which is what I do. You can even use something like a refrigerator shipping box for a brooder. It's good to get it set up and the temp checked out before the chicks arrive. We have a whole section of brooder designs to give you ideas.
I brooded 25 in the house in a cardboard shipping box with bird netting over the top for a few weeks. One feeder and two waterers from the feed store didn't cost much. Those quart waterers are small, get filled up with litter quickly and require attention several times a day for them not to run out of water. I'd get the white and red plastic type that
TSC carries, one of each, about gallon size, and be prepared to raise them up off the litter in a few days. Put some marbles in the water base for a week or two, as they will fall asleep while eating or drinking when young, and can drown. I use the pine shavings
TSC sells for litter, which many people do. You can use dried leaves, hay, sand, shredded paper, almost anything, though the pine does help control odor. Be sure the room or area gets a nice supply of fresh air, to help clear the pine odor and dust. Feeding is simple enough: starter for 4 to 8 weeks, then grower, then layer around 20 weeks or when they start laying. You can also feed the starter feed til they start laying. In my area they sell a starter/grower formula that is fed til it's time for layer. You don't even have to feed layer after they start laying. You can feed grower or flock raiser. But layer has extra calcium so if you feed, say, flock raiser, which is better for the roosters and sometimes the hens as well, you'll need oyster shell offered separately for the calcium. The only other thing you need is grit, also offered separately, but you don't need it with starter feed, and depending on your soil type, you may not need it at all. If there is granite or other hard rock, or even lots of sand, you probably won't need any. It's sand and limestone which is soft where i live so I offer some grit -- but mine almost never take any, and I've never had a crop or digestive problem. Treats aren't necessary but you'll probably want to give them some. A great beginning treat is plain yogurt with a little chick feed and maybe water mixed in. Also something like oatmeal with yogurt. Yogurt or organic apple cider vinegar (ACV) in the water (about 1 Tbsp per gallon) are both good ways to provide some probiotics to young chicks, a good thing. There is a treats chart on BYC. Chickens can eat most anything you do except chocolate; a lot of sugar or salt is also not good. Of course when young, small soft bits are safer. A safe rule is, don't give treats that total over 10% of their intake, because their diet might end up deficient in something otherwise.
That would be a cute coop, but very tricky to build unless you have an experienced carpenter around. And the yard will probably be too small. Everyone loves to eat chicken, and you'd be surprised what will come out of the woods when there is chicken on the menu. You may find free ranging leads to losses and give it up. As a rule of thumb, figure 100 sq ft in the coop for 25 chickens, and 250 for the yard or run, but this depends a lot on climate. They will stay in more and do better in a larger coop in a climate that gets snow, although they will probably still go outside most days unless you are in Canada or Alaska. Where I live they actually only need a 3 sided structure and would be fine with 2 sq ft per bird in the coop, if well designed to keep things dry when needed, prevent draft on the roost on cold nights, and to keep the feed dry. A 3 sided structure can be predator proofed by extending the wire out from the coop.
For 25, I'd build an 8'x12 ;building with the roof slanted from one side to the other as this makes ventilating the coop simple -- and ventilation is necessary even (or especially) in very cold climates. Even up north I'd leave the upper soffit area open air on one side. A coop should have natural lighting. You can secure a piece of plexiglass or glass to the building, or secure hardware cloth then have a wood shutter, there doesn't have to be a real window. Or fasten hardware cloth over a hole in the wall then put plexiglass in a simple wooden frame to close it if needed. It it's downwind, you may not need to close it at all. If possible, wire and plumb your coop, or wire it and have a faucet just outside; saves an awful lot of work.
Where I live, some old timers just have a fenced area with a piece of weighted down plywood over part of the top; no sides. It's hardly an ideal setup and I wouldn't give mine that little comfort -- but adult chickens can thrive for years in such a setup. They don't need heat (except as chicks) but do need shade and breeze in the summer, even, say, in New York summers, as they tolerate cold much better than heat. There will be times you want to turn on a light at night, besides power for brooding, and you may decide to provide winter supplemental light for increased egg production. I don't, but mine lay enough pretty well year round except when molting.
Chick sexing is about 90% accurate so unless you buy all sex links, you will get a rooster, believe me. Even with sex links, if they send a "free fancy breed," or put in a few extra as they often do, those will be roosters.
That's really just some introductory thoughts to get you started. Check out the stickies on the various forums, and the learning center, coop section, etc. and you will find loads more. Everyone does it a little differently and, with some basics addressed, they can all work.
Good luck on your chicken venture!