You want to get a few quotes and then leverage the best quotes to see if other lenders will match or beat them.

I would not recommend getting a loan from a "big name" bank. Their rates are not the best and they don't have much room for negotiation. A broker is going to be your best option.

Check out www.better.com - their rates are very competitive and an easy way to get a baseline quote.

I've used Harborside Home Loans several times (current home purchase and two refis on my previous home) and they are fast with closings in about 3 weeks or less: https://harborsidehl.com/

Better offered me a slightly better rate but Harborside matched it.

Keep in mind that once your apply for a quote, that information goes public and your phone or email will get blown up by other lenders trying to get your business.