@arouechYes bigger is better. Chicken math is real!

I was lucky enough to have a coop on the property I moved into. I do think a prebuilt shed is a good starting point. You can often find them for sale on Craig's list or last years model from a store that wants to get rid of them.
I never wanted a rooster and ended up with 2. I even tried giving one away but he's still here. They can be a great addition to the flock but they are not perfect protectors. You still need to protect the girls and sometimes that includes from the rooster.
You can find them for free. Just be careful with bio security. If you can quarantine a new bird you should be fine. If not boys are usually sold for half the price of a pullet.
Have fun with your flock!