I was invited to comment and am pleased to offer some basic advice. I may contradict what some of the real estate agents have told you so I don't mean to sound petty.
You do have an excellent credit score, however, the days of great credit scores getting you the best loan terms are gone. Now, more than ever, lenders are returning to old school underwriting and the ability to repay the loan, as measured by a debt to income ratio, are essential.
NB- My advice is general because prescribing a specific solution, on a website like Trulia, is like treating a disease on WebMD. The absolute best thing you can do is have a mortgage planner help you with this personally. I'm happy to advise you; click my link for contact information.
1- Pay down but don't pay off the installment debt. If your balance reflects less than 12 payments due, it will not be counted in your ratios by an underwriter. The lower balance, when reflected to the "high limit" will maintain your excellent credit score.
2- The revolving debt can be strategically paid down to reflect lower payments. If you pay an account down do NOT close the line of credit; that will eradicate "available credit", causing the algorithm used by the credit scoring models to think that you are less credit worthy than before.
You've done an excellent job managing credit to date. With personalized counseling, you'll position your self for the best home loan available.
This math exercise assumes that an 80% Loan to value loan (Purchase with 20% down) can be obtained for a note rate of 6%, I then assert that the same borrower can qualify for a 95% loan (only 5% down). Due to the higher loan to value ratio (and perceived risk by the lender) the interest rate for the 95% loan is 7%
If I "unblend" the 7% rate on the 95% loan. I discover that the first 80% of the purchase price is still at 6% but the additional 15% of purchase price is actually at a cost of 12.333%
If the borrower has to borrow the higher loan percentage because they want to use most of their down payment money to pay off their automobile and credit cards, one of the questions I would ask, is: " Are the interest rates of your car loan and credit cards lower or higher than the 12.3%"
This math problem does not contradict the excellent advice given earlier by Brian, Ute, Sylvia, and the others. What is best for you personally may not be the best for someone else in a nearly (but not completely) identical situation.
Having a 780 credit score while carrying both auto loan and revolving credit card loan should not be a problem for you because 780 is a great credit score. Perhpas that money can be saved for downpayment, closing cost, etc..
However, I am not a mortgage broker; so, I contacted a couple of mortgage experts in Trulia for you. Hopefully they will come and give you their professional opinion on this.
I am assuming that the auto loan is already amortized and I would check to see whether paying down the principal will automatically lower your monthly payment or whether the lower principal will just mean that you'll pay off the remainder sooner. For instance, when you have a fully amortized mortgage, paying off the principal just shortens the life of the loan, but does not affect the monthly payment. You'd also want to make sure that there's no prepayment penalty on the auto loan. I would not want you to pay down the car loan and then find out that it did not have the desired effect.
Checking with a mortgage consultant first will also help you decide if you have to do anything. The mortgage consultant may advise you that it's better to use your savings to buy down the interest rate on your future home loan or to put more down on the house to avoid having to pay private mortgage insurance. If you end up paying down the credit card balances, you'll free up additional credit for future use while paying down the auto loan does not have the same benefit. Good luck to you and it would be great if you came back to Trulia to let us know what the mortgage professional recommended.
You will see CMPS next to that persons name on a buisiness card.
Every situation is different and the formula for calculating a credit score is very complex and almost impossible to understand (especially when you try to use common sense!)
If your income substantiates it you do not have to wory about paying off any other debt unless it affects your debt to income ratio.
You are fortunate. Buy a home and ride the wave up... yes this is coming... be ready for it.