Another question - would a large metal dog crate work for a brooder (going to use a brooder plate), or will they just pop out the sides? I'm not sure the brooder box I made is big enough for the chicks we'll have in it (it'll be OK for 3 chicks, probably not for 7, and definitely not for 7 "teens".)
I could tie some hardware cloth to the sides if it is a problem - I don't want the surprise of a chick in my cat's jaws.
If you have a cat, even with HWC on the sides, I'd be concerned about him reaching in from above. Those chicks are going to be irresistible to him. Many folks do use a dog crate, and zip tie HWC to the sides. But, in your case, with cat... I'd not go that route.
Do you have a garage or a shed? Is it fairly rodent proof? I'd not worry so much about mice, but RATS could be chick killers. If you have a garage available, or a closed in porch, or some such, you could brood them there, and keep the mess out of your house.
Sometimes, I start chicks in an appliance box in my garage for a few days before moving them to the coop with their heating pad brooder. You can cover the box with a secure screen, or a chicken wire top... or what ever secure (cat proof) cover you can come up with. It will provide much more room, and you can easily add an extra box if you need the room! If you've not yet bought your heat plate, I urge you to read Blooie's article about heating pad brooding. And she has a thread dedicated to the same topic. A heating pad provides a wonderful broody mimic for a fraction of the cost of the plate.
As for your coop, think outside the box: Sometimes you can buy a shed from Lowes, Home Depot or a competitor for about the same price you could build a similar sized structure. End of season, they may be marking their models down to get them out of the parking lot before snow season starts. Minor modifications in terms of extra ventilation, perches, windows, nest boxes, water proofing floor, and you're ready to go with a finished coop. You might even find a used shed that could be moved without too much work. For 7 birds, I'd be looking at a minimum of 4 x 8 foot print to allow a bit of extra room for feed storage, a broody cage, or any future flock expansion.