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What matters most? People will get this wrong. It's not rate and it's definitely not closing costs. Rate is the 4th most important factor and closing costs come in 5th. It's actually your future financial goals, term (length) of the loan, and savings over the life of the loan.
Be prepared to share your future plans with your mortgage banker. There are many programs, so there are many rates. You don't have to divulge personal info, just keep it general.
Don't just ask the rates. Let the professional know what you want and pretend like you don't know everything. Take in what they have to say just in case you are missing an important factor. This is a great way to check yourself.
On the other hand, if you know the terms or loan program you want because you have done your homework, let the sales professional know this. Ask if there are any specials.
When purchasing a home lock a market rate and cinch the home. Do yourself a favor. Don't let the rates dictate a purchase, they have time restraints. Adding rate shopping to the purchase often causes additional pressure, disappointment, and could cause you to miss a closing/commitment date. A general rule of thumb is to shop for the bargain rate after you own a home. This doesn't mean you won't get lucky during a purchase.