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from a credit history or credit score standpoint, is having a car loan considered to be "better" than having a credit card debt?

Generally, yes. A car loan is an "installment loan", and having different kinds of loans can help the credit score. If it is the choice of one or the other, the car loan is probably better. However, generally an account will appear on the creit report up to 7 years after the date of last activity, so paying off a car loan does not necessarily mean you lose the benefit of that loan in determining your credit score until it ages off the credit report.

A credit card account, on the other hand, is a "revolving debt" that can be added to at any time. As one other reply indicated, car loans, student loans, mortgages are usually considered "less bad" than credit card debt.

Which loan should I try to pay off first each month with my payments over the minimums?

As long as I never miss a minimum payment due and my debt is not increasing (and preferably with my total debt decreasing), I would probably not worry so much about the credit rating unless marginal for qualifying for the best rates on a mortgage.

As per the numbers were presented, paying off the car loan is probably the least-expensive approach unless there is something "odd" about how interest is calculated on the car loan.

On the other hand, some credit card companies are very devious. If you charge something on that card, it will probably go on at a higher interest rate, but the payments beyond the interest will go to the lowest interest rate debt first. (This is one trick a credit card company has of turning a nice 4.9% balance transfer to a high interest income to the card issuer.) Another trick is to delay posting payments by a day and, if one is close to the due date when the check arrives at their designated payment location, they may use that to charge you a late fee and also increase the interest rate. (I have heard of cases where the payment was posted to the credit card account several days after the check was posted to the checking account--the credit card issuer backed down on late fees when the complainer said s/he had proof that the check had cleared before the due date.) The really bad companies "forget" to send a statement so the minimum due payment is missed. (Alas, you are responsible for payments, whether or not you receive the statements.) So, if you are distrustful of the credit card issuer, it may be better to just pay off the card so you can be at peace about it.

I guess that means it is your choice on what you pay down first.

My recommendation would be, once both are paid off, to start making "car payments" to a savings instrument (money market mutual fund, money market deposit account, or even a regular savings account) so you can earn interest on money to be used for buying the next car instead of paying interest after the next purchase.
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