Potential lenders want to know that you will continue to pay your loan as agreed for the long-term, not just the short-term. The more time that passes with positive reporting on your loan, the better it is when it comes to improving your score.
You are also correct that you need to add some revolving accounts to your credit history. Ten percent of your credit score is calculated based on new credit and another 10 percent is based on type of credit. You need to have different types of credit to receive needed points on your score.
Creditcards.com has several recommended credit cards for persons with no credit history or insufficient credit history like you. Your goal is to acquire a card with the highest credit limit for which you qualify with the best terms for you. Once you have a card or two, keep your balances very low, if you plan to carry a balance, and make sure you pay on time, every time.
Keep in mind that the interest rates on the credit cards for which you will qualify with an insufficient credit history will be on the high side. Make sure you can afford the payments at the higher interest rate if you are going to carry a balance.
Your checking account balance and activity is not factored in your credit score. However, your income and banking habits are reviewed when you apply for credit. So keep up the good work with your banking account as it does improve your creditworthiness, even though it doesn't improve your score.
One other thing is working in your favor. Although the credit cycle has tightened up a bit due to the threat of recession and the mortgage crisis, the recent rate cut by the Federal Reserve has lowered interest rates across the board. Keep up your work on improving your credit score and with the Fed's help, it should be easier to refinance at a more affordable rate in the near future.
