You are building a credit rating by paying on your credit card on time, whether you pay the minimum or full amount, you're demonstrating that you are able to both afford the minimum payment and are responsible in meeting obligations.
This strategy, however, can only go so far. Your ability to obtain credit is based also upon your ability to repay, which includes both your cash after taxes and other obligations and your tangible assets. Consider if you came to someone asking to borrow $10,000 yet you had no assets to back it up (that is, that I could legally take away from you if you didn't repay me) nor did you have an income stream that could meet the minimum payments.
My suggestion is three-fold:
- Continue making solid payments on your existing obligations
- Build tangible assets (a substantial savings account)
- Increase your income
Yes, obviously the last one is somewhat out of your control, but it is one of the keys to obtaining larger lines of credit.