Unless you plan on getting a lot of mail or not checking it often, the smallest size box should be sufficient. That's what I have. Any packages, they typically pass over the counter to you or put in a special box for packages (and stick the key for it in your PO Box)
When you sign up, they ask if you'll be getting mail for any other names. Be sure to give your business or fictitious name then. Will save awkward questions later.