NEVER use a debit card. NEVER.
Debit cards do not have built in fraud protection. My bank charges $11 a month for it.
Use a credit card, and if you can't get one, go secured. My credit score was 810 after 2 years on a secured card. Secured does not mean a lower score versus a regular CC.
Interest rates are shit, so trying to keep the highest balance in an account and only taking a little out via a debit card as it is needed is meaningless towards your credit score or interest.
Running a balance is also a bad idea, if you can pay it off. CC companies make their money off of per-transaction fees from businesses. Sure, they would like you to pay interest on balances, but at the end of the day, that 10 cents from each transaction is more attractive than having their money tied up, and the possibility you may default and your account may need to be sold for pennies on the dollar to a third party collection agency.
I get platinum offers at least three times a week, including from my current CC company. I take out $1,000 a month in cash for groceries and day to day expenses, and NEVER use a debit or ATM card.
If you don't believe me, it's pretty easy to prove. Try it for six months.