It’s not nearly as much about supplies as techniques and what to watch for. You already have more supplies than I normally start with. I don’t do the probiotics. Read through the Learning Center on the top of this page to take advantage of others opinions and experience but expect conflicting advice. There are many different things that can work which means there is no one right away to do much of anything where everything else is wrong. There are a lot of right ways to do about any of these things. For example, look through the brooder section. You will see a lot of different brooder set-ups, some with totes and some using other things. Some brooders are in the house, some in a garage like you intend, some in the coop or other outbuilding. There are a lot of different ways to warm the chicks, different ways to feed and water them, different bedding used.
I don’t know how many chicks you intend to get or the physical dimensions of that tote. Lots of chicks are raised in totes like that but they grow really fast. They can outgrow it or fly out of it really quickly. Be prepared. In my opinion, your main goals with a brooder should be to keep it dry and to only heat one area, letting the rest cool off as it will. A wet brooder is a dangerous brooder, both for disease and even foot damage if they stay wet. If you can keep one area warm enough but other areas cooler the chicks will self-regulate. They will go to the areas they are most comfortable. Ideally that is all over the brooder. If they are too cool they will bunch up near the heat, too warm they line the wall as far from the heat as they can get. If it is about right they will play in the cooler areas and go back to warm up when they need to. They probably will sleep in a group near the heat, not because they are cold but more that they like each other’s company. Watch your chicks and let them tell you how much heat they need. That’s much more reliable than trying to keep everything a specific temperature.
Your breed selection is fine. It should give you some really interesting eggs and they should get along well. You are correct that you can expect cockerels. You need a plan for those. Don’t count too much on them being 50-50 though. My hatches are more likely to be 2/3 cockerel or 2/3 pullet rather than split down the middle. Last year one hatch was 14 pullets and 7 cockerels. Another was 9 pullets and 3 cockerels. I’ve had plenty where the majority were cockerels.
I venture to say the vast majority of us that hatch our own chicks do not vaccinate them for anything. I’m not opposed to vaccinations, especially if you know you have a specific problem in your flock, but a lot of chickens are never vaccinated and don’t have problems. It’s not something I’d be over-concerned about right now.
One of your risks in raising them is Coccidiosis. The bug that causes Cocci can live in the ground anywhere but it thrives in warm damp soil like the Gulf Coast, in the bottom of a wet brooder, or in a wet coop or run. You need to learn the symptoms and what you need to do if it shows up. What normally causes the problem is the chick eats some of the oocysts (eggs) that cause it, they hatch in the chicks gut, and the number gets out of hand. After two to three weeks of exposure they develop an immunity to that specific bug so it’s not a bad thing for them to be exposed to it at a young age as long as the numbers don’t get out of hand. The way I manage this is to feed them some dirt from the run where the adults live while they are in the brooder to expose them to it but keep the brooder dry enough that the bug does not thrive. By the time they leave the brooder and hit the ground they already have immunity. It’s also very important to keep the water very clean. With your waterers change the water out completely every day. I don’t use medicated feed but some people do. It does not wipe out the Cocci bug totally, it allows enough to live so the chicks can develop immunity, but it reduces the numbers that reproduce so the number is less likely to get out of hand. You still need a dry brooder.
There is one supply you don’t mention that you need. If it’s not prepared, get your coop ready now. They grow awfully fast and you may need that coop a lot sooner than you think. If you can provide heat in the coop, you can start them out there instead of in your garage, but with your kids you probably want them more accessible to start with.
Good luck and welcome to the adventure. It’s a fun ride.