Creditors want to see your ability to pay on time, and effectively manage the credit that you already have. So, being late, especially on a first mortgage, is a huge hit. Also, they want to see that your ratio of "what you owe" to your limit stays under something like 70%. So if you have a CC limit of $1,000, you're best-off to never owe more than $700, but it's also advisable that you don't pay off the balance either (see how you're doomed to fail???). Sometimes, you can simply "cheat" and as the CC provider to raise your limit, which improves your ratio, which improves your credit score.
Opening a new CC hurts you, closing an existing CC hurts you. You cannot win! It's like the Kevin Trudeau infomercial that runs on tv; the lower your score, the more money they make off you (due to higher interest rates).
In short:
Keep a mix like mortgage, car, CC
Keep the debt-to-limit ratio down, but not 0
Pay on time.
Some credit reporting agencies will accept on-time paying of utility bills to enhance your credit score.
You can use a company like LexingtonLawFirm.com to help eliminate negative items from your report. Figure about $40/mo for about a year to make some real progress.