How many open accounts would I need to raise and maintain my credit score?

I have a fair credit rating in the low to mid 600s. A couple of things affecting my credit right now is my credit history is between 2-3 years old. So I know that the longer I have this credit history it will improve my score. I also had some hard inquires on my credit report recently. A few months ago, I had to put maintenance into my car and fell behind on my college loan. It does show up on my credit as a late payment but I was able to get a forbearance.

Recently I came into some money and paid off all my bills including my car payment, my college loan, mortgage and credit cards. Right now I am debt free but foresee having to get a newer car within the next two years.

Even though I have my debts paid off, I want to get my credit score to higher than what it is. Many of my accounts are closed except for the credit cards. How often would I have to use one? I have several through different stores and banks.

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