It sounds like you might be biting off more than you can chew. It's really a good idea to have your brooder ready first and all warmed up for when you bring your chicks home. A monitor box doesn't sound very big. I used the largest size Rubbermaid tote (18"x36") for only 3 chicks and that held them ok for about 4 weeks before moving them outside to the coop. The dust and dander inside your home becomes unbearable (at least to me)... totally different than dogs or cats.
I hope you have a big backyard and a really big coop planned. I think 5 or 6 chickens to start with would give plenty of eggs for your family.
Best wishes in your new chicken adventure!
Hello and welcome to BYC! Glad you joined.
How many chickens you get is dependant on how large a coop and run you plan to build. That cart before the horse thing usually ends up with one frazzled chick owner desperately trying to get the coop built because their dining room is becoming a dusty, stinky mess with a bunch of hyped up chicks flying around. Good luck!
Make sure to check laws and ordinances in your area for owning poultry. This may determine type of housing, location on property, number of chickens, sex, etc. Need to check with local planning commission to determine if need to file for application or permit to own poultry as these are sometimes needed.
It's nice to have you here with us! Starting with 6 seems like a manageable number, you can add more later if you want (and most people do). Do your homework and read up on the information others have posted links to, feel free to ask questions.
Hi and welcome to BYC We're so happy you've decided to join us
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Welcome to BYC! Glad you decided to join us. Definitely go with 6 to start. Find a brooder plate and ditch the heat lamp. The heat lamp will make your electric meter spin out of control. Also with all the dust the little fluff balls make it is a fire hazard as well. Get an air purifier to help deal with the dust. I did the same as you, getting the chicks before I had everything set up. It is a little stressful but survivable. Go over the coop design plans carefully and ask our experts any questions you might have. That's what we're here for. Good luck in your new adventure in chicken world.
Glad you joined.
to have you here with us. Enjoy your time here at BYC! 
