Getting them from the mail would make me nervous. Whereabouts are you located? I'm in Texas and at this time of year it gets way too hot.
I got started with quail with brown Coturnix adults from a farm store and Texas A&M Coturnix chicks from a nearby ranch. Brown Coturnix quail can be sexed as soon as they get their feathers, since the boys have red chests and the girls have a consistent pattern all around. Texas A&M quail can't be sexed until they crow/lay, unless you look under their skirts. I just started hatching brown x A&M chicks a few months ago.
I hatched mine unusually. For my first batch, it's so hot and humid here during the day that I didn't need a heat source in the afternoons. In the evenings I used a heat pad with a thermometer to make sure the temperature stayed around 99F. I turned them every few hours. All three eggs hatched. They started in a rubbermaid tub. Quail chicks are very cute but they get confused very easily. They often got lost behind their water or just standing on one side of the tub slightly behind their newspaper bedding. One chick died in a freak accident: she somehow wedged herself between the water dish and food dish, and it looked like she broke her own neck trying to get out.
My second hatch, which I am raising now, I used a broody silkie chicken to sit on the eggs. All 6 hatched. I left her with them in a rubber maid tub the first few days, then moved them all into a 4'x4' cage for a few days, and now she is raising them in the kitchen garden (20'x20'). No accidents: having a mom with them constantly helps them out. Most of them have even learned to speak chicken. They are getting pretty big and flighty, so in the next week they will have to be moved into the quail area. If you have a small broody hen, I strongly recommend using her for quail! This batch of bird-mothered quail are having a wonderful time and are noticeably more adventurous, observant, and social

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For food, I just let regular sized crumbles sit in water, and the chicks don't have problems with the mash. I use a game bird feed that is 25% protein. For water dishes, I used jar lids for the first week, and a regular chick water dispenser after that. Newspaper works well for bedding, since you can change it frequently and they can't kick dirt into their food/water. For the first week, I would keep them somewhere relatively small. For my first batch of motherless quail, I put dirt all in the bottom of the tub after I saw them attempting to dust bathe on the newspaper, lol. I think they were just over a week old. They moved into the outdoor cage with the female quail when they were 2.5 weeks old, and have gotten along well.
Are you raising your quail for meat or for eggs? Either way, you are going to have to kill most or all of the males you hatch. It's sad, but the males over-mate and peck at the females, and fight brutally with each other. They are worse than roosters by far, in my experience.
How big of a cage are you going to use? I have an 8'x4' outdoor cage which works well for my small flock of never more than 12. It's unfortunate that they can't be free ranged like chickens. If you are only going to have a couple (for eggs), you could keep them wherever, as long as they have around 2 sqft or more space per bird, clean dirt to bathe in, and plants/things to hide in.
PS Just like with baby anything, whether you use a mom animal or not, you are going to need to be there to supervise most of the time for at least the beginning.
PSS I wouldn't bother with any quail cage you can buy online. They are too small. It is a good idea to have more than one cage though, in case you want to keep more than one male with a few females, or you want to pull out males and wait a bit before butchering, or you need to quarantine someone.