A lease will show up as a loan on your credit report. If you're way over the miles, just buy out the lease from the leasing company and convert it into a loan (this is what I did!). Or a few months before your lease is over go to a dealer and say you want a new lease.
I feel a lease is terrible no matter the terms. It’s not going to help your score either, not like a loan would. And I’ve seen too many times, at the end of the lease, someone having to pay thousands of dollars for overage on miles or minor damage.
A local bank for a car loan is probably the easiest to get based upon score. I know my local bank approves at 625 for 7-9% interest on used cars. My done got a 6% for a car 2 years old with a 740 score.