Even if you do earn 15% on your stocks, your interest paid out on the credit cards is 18-22% (depending on the company). Just by comparing the figures, you see that anything you earn will be eaten up by the interest on your credit cards.
We have all heard the statistics that a credit card balance like yours will be paid off in at least 30 years, at mininum payments.
In addition, the margin investment is another form of debt. You will increase your total debt without dealing with the previous debt. A margin call will be potentially devastating (at the time, you may not have the cash to cover it).
In short, get rid of the debt; then invest what's left. Even if you go with the margin account, that will be the only debt requiring your attention.
Income Tax Preparation. Life, Accident, and Health Insurance. My desire is always to help.