For the maximum number of available credit score points due to utilization you want 1 card to show a small balance and all other cards at a zero balance. That is assuming you have at least 3 cards. You also want less than 8.99% total revolving utilization, and less than 29% on any single cards utilization. Your scores right now are more than enough to receive the lowest interest rate. Usually the best rates are from credit unions. I received a 1.99% interest rate for 100% financing of a used vehicle. I think the interest rates have gone up since then, but that credit unions rates are still the lowest I ever see. You also need to be careful that the lender is not considered a consumer finance company. I learned the hard way that Honda Financial is considered a consumer finance company. The mere presence on a credit report of a consumer finance account is seen as a negative on some versions of fico scores, even if it has a perfect payment history. I have never understood why that is the case, but I know that it is the case.
Everyone has a different opinion. I check all three of my credit unions about current rates and use the CU with the best. Have them pre-approve me for a loan amount, rate and loan term I want. When I go shopping I know everything I need to know, and am ready to pull the trigger. Some times I let the dealer shop for a better loan but have found that most of the time the dealers loan rates are not enough better to use the dealers financing. Kia and Capital One have come back saving about 1/4% but those are only two time over about 12 cars. Is 1/4% worth the extra HP's? All of my CU's will pre-approve with soft pull, so I only take a hit if I buy a car. If I let the dealer check I sometimes have a couple of HP's.
PS: Check CU's auto, personal and secured loans before joining.
I have a couple of CU's that are worthless except for borrowing money but when you need a loan they are nice.
I would highly recommend going over to the Leasehackr forum if you are looking at leasing. Lease rates can be different that finance rates.
This is a piece of cake...
First of all, don't even worry about paying down your credit cards. Your debt-to-income will be fine and you're also in the highest tier possible being above 750 on all three bureaus... Secondly, when negotiating the price on your new vehicle, negotiate from invoice, not from MRSP... whether you're leasing or financing, dealers have something called "dealer cash" when they sell new vehicles... this can be used to essentially reduce the amount you're financing. Do some research into rebates, incentives, consumer cash, dealer cash, etc. on your new vehicle.
Dealerships also occasionally offer 'subveen rates' i.e. 0%, 1.99% through their captive (in this case Chrysler Capital)... ask about those first, if not don't take anything above 4-5% MAX.