How do I pick the best refinance lender?

I'm 4 years into a 30 year fixed mortgage with Wells Fargo, at a 6.75% interest rate. With rates around 4% now, I ran the numbers and decided to refinance.

This is my current breakdown:

Monthly Principal & Interest: $1,807.07
Total of 360 payments: $673,225.37
Total interest paid: $384,900.37
Payoff Date: 9/2037

And the breakdown with a 4% refinance I calculated online:

Monthly Principal & Interest: $1,308.3
Total of 360 payments: $470,987.24
Total interest paid: $196.949.54
Payoff Date: 11/2041

I did a basic search online and found lot's of refinance options, many from lenders I'm not familiar with. They all had around 3.8%-4.0% rates with varying amounts of APR's. Some of the APR's were even $0.

I want to just pick the one with a $0 APR and the lowest rate, but I'm not totally sure what I'm dealing with. How should I go about figuring this out?

I figured I would just do a little research on the lender and then talk to them to see what other costs there would be associated with their offered rate.

Also, I've also seen FHA loans at 2.0%. What's the opinion on those? They seem way too good to be true.