When it comes to financing a vehicle, most of the time we want the lowest down payment possible with a relatively low monthly payment as well.
When it comes to a vehicle loan down payment and monthly payment have a direct effect on each other.
The best way to think about how they affect each other is to think of it like a seasaw. The more money you put down will overall lower the monthly payment for the term. However the less money you put down, the more money you will need to put up on the monthly payments.
One of the biggest risks when putting down a little to nothing down payment is being "upside down" meaning you owe more on the loan than the vehicle is currently worth, also known as having negative equity. When you have negative equity it can make buying a new vehicle even harder.
For example:
You buy a car for $30,000 for a term of 72 months with $500 down. You enjoy traveling and in 2 years manage to put 70,000 miles on the vehicle. You decide you want to buy a new a vehicle $for 32,000 and you get a trade in offer of $13,000 but you still owe $23,800. The $13,000 is put toward the payoff loan and leaves you with negative equity of $10,800 which will then add to the new vehicle, potentially preventing you from a lower interest rate or even an approval. You would be financing not $32,000 but $42,800 and that can result in more money down required, more financial hardship, a higher monthly payment, and the possiblitiy of not being able to dig yourself out of the hole.
Although saving money and putting a smaller down payment might sound better, in the long run the more money you put down might be more benificial to you.