The big three will snatch it up after sure, but the right lender absolutely does matter a whole lot in terms of the rate and relationship and you are asking the right question. We went to three lenders, one of them had a rate much lower than the others, and also offered much lower terms on mortgage insurance. They also were local, knew our realtor and their way around things. We were ready to close in no-time.

The other people we went to were rude, gave much worse rates (think 10% higher), and also accidentally emailed sensitive documents to randos they used to work with (these people were with FirstHome, which I see is getting a lot of positive reviews below...so the individual really does matter).

Anyway, my wife and I can recommend this guy: https://www.primeres.com/chadpiunti

try checking out a credit union - like State Employees Credit Union. One thing though, it seems some seller agents didn't want to work with them and since I didn't really know what I was doing, I just said ok, and worked with someone else. I assume this is because there are certain lenders that will approve anything and they were afraid of pushback from SECU. i encountered 2 sellers agents like this. I also tried using M&T, which a another sellers agent wouldn't use as they said they weren't local (?!?!). This was at the height of the housing market boom though, so things may be different now. I ended up using the lender the sellers agent wanted me to use and my loan was sold about a month later...and then again a month after that - which is exactly what I was trying to avoid.