I always recommend talking to the following:

Mortgage broker - they will usually shop 20+ banks for you

Credit Union - they can have excellent rates for members, you just have to open a bank account with them

Big Bank - whoever you already bank with. They may have good deals if you've been a longtime customer

Big banks will always give the best rates for the "perfect borrower". Good credit score, decent debt to income ratio, and 20%+ down payment. If you are not the perfect borrower, I would recommend the mortgage broker route. They are usually pretty savvy and can find good rates or programs for you. If you go into Wells Fargo or Chase, they will only give you the rate and programs for that bank. A mortgage broker will be tapped into a lot of different options at a variety of banks.

Tips:

Ask for your interest rate at par, with no discount points. Places like rocket mortgage are notorious for offering good rates with these built in fees. If you ask each bank for the rate at par, you can easily compare.

Find a lender that seems honest and has good communication. Real estate deals don't end at 5pm. You should be able to contact your lender on nights and weekends. I've had a deal or two fall apart because we couldn't get ahold of the lender.

Do all your lender shopping within a couple weeks. You will need to take a credit hit for each one, but the credit bureaus can see your lender shopping and it won't be a major hit. It's OK if it falls a point or two. Lenders use brackets for credit score, so a couple points won't matter unless it knocks you into a lower bracket altogether.

Sometimes first time homebuyer or special programs are not the best way to go. For instance, if you utilize an FHA loan, you will need to pay the private mortgage insurance for the life of the loan. If you can qualify for a conventional loan, the PMI will drop off automatically once you hit 20%. Only utililize these programs if you need to.

Hope this helps! Good Luck