Get auto loan first or meet (private) seller first?

Factual Questions
1

It has been about 11 years since I’ve bought a car using a auto loan rather then cash so you’ll have to forgive me. I don’t remember how I did this last time. Should I go meet the private seller, check out the car, and negotiate a price first? Or should I go to the bank and apply for a auto loan first?

I have enough cash in my account to pay for it in full but I plan on buying a house in a few months. Will having the auto loan have a negative effect on my chances to get a mortgage? The car I’m looking at is about $6500 offered.

2

I’ve heard that you shouldn’t apply for credit for 6 months to a year before trying for a mortgage so I’d try to buy the car without a loan.

3

Pay cash, no car note. As long as you’re convinced of the car’s longevity, usefulness, etc.

4

A mortgage company is going to look at both your outstanding debt and your assets on hand. I’m not sure if paying cash is necessarily better than buying the car with a loan, especially if you’re only talking $6500.

My real advice is to find a broker and get advice from the source. Good brokers are an asset to help you choose the right loan, get your finances in order and set yourself up to look good for the underwriters; they’re not just there to execute a few pieces of paper and collect a commission.