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Lowering your util will increase your FICO score, so that would obviously help your interest rate when being financed. However, saving up a down payment, would lower the amount financed, lowering your interest paid, and larger down payments can help if you are borderline on approval.
My person opinion; pay down your CCs. You are paying interest every month on that debt and need to get it under control. That is very high utilization. Down payment does not affect a car finance that much usually, so don't let that drive you.