Afaict, your credit score will likely be lower if you haven't had a credit card open for a long time, run your balances too close to the limit (available credit) on those cards, or don't use them at all. My understanding is that your bills, depending on their type, may not even bother reporting to the credit agencies, or only report when they believe you have failed to pay; reliable ones seem to be big loans like mortgages, student or auto loans, and then credit cards. Rent, utilities, etc haven't seemed to affect my credit positively (or if they do they haven't been noticeable compared to the first category)
When I graduated, rented, and paid all my student loans off early and did not have a credit card my credit score actually went down significantly until I opened credit cards and used them regularly.