Which is the better option, Money market account in my business (S corp, sole owner) name or personal?

keep your personal and business expenses separate. what type of account your s-corp has is irrelevant as long as it's in the name of the corp. 

try to avoid mixing business and personal expenses in one account. you will create a nightmare for yourself should you be audited.  This doesn't mean that you can't take distributions from your s-corp but it's best if the money goes into a personal account to pay personal expenses.