That sounds like a max of around 6. Would second the advice to build bigger if you can to accommodate chicken math! I have six and am maxed out on space as well. One thing I did not consider getting them all at once that, assuming you don't lose to predation or illness, your egg production is...
My lazy chickens are definitely not up at dawn. Husband used to open the door at 5 and they weren't up. Now we have an automatic door that opens at 6:15 or so and they still don't necessarily barge out the door. So don't feel too bad if you aren't always up at the crack of dawn!
If you think you even MIGHT be OCD about picking up poop on a daily basis (or, er, multiple times/day), make sure you can easily reach all parts of the coop/run. Although I think chicken math considerations top the list!!!!