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I have leased a few cars, and it reports some what like an installment loan but worse.
So lets say you lease a car for 30k and put nothing down. And lets say the cost of the lease is 2k. It would report on your credit as owing 32k. And since lease payments are typically smaller then a purchase, it takes a long time to bring down what you owe.
At the end of the lease you would owe like 15k, so you either pay off the 15k, trade it in or return the car.
Typically you don't want to do any big moves on credit before getting into a mortgage. You also seem to be more worried about total debt owed vs your DTI. The amount you owe is less important vs the size of the payment.
But your scores are very good, you have some wiggle room to work with when your score drops from a new autoloan. I would only do it now if you are worried about your DTI and need to get your payments down.
Not just the full 35k, but whatever the lease cost is as well. The money factor works differently then interest, so they put the lease cost on top of the full amount.
The last car I leased was 40k and the cost to lease was 5k, so it reported I owed 45k. It really sucks.
Also don't be concerned about the amounts you owe, the bank doesn't care. They look at the DTI.
The only time the amount owed is looked is if you are a few months away from paying off an installment and they remove it from your DTI.