We want to buy a home and were told the first step was getting
pre-approved. Then we were told no, we should get a pre-qualification
letter because that won't ding our credit.
Pre-qualification doesn't ding your credit because it serves very little purpose. In a pre-qual you provide your numbers for income and debt, and they give you an estimate of the amount of loan you can get. It is based on you being forthright and compete in the numbers you provide. They do no checking to confirm your numbers. They don't access your credit score and history so they have no idea what your credit worthiness is. A pre-qual doesn't impress sellers with knowledgeable agents because They have no idea if you will be able to get a loan.
You want to get pre-approved. They will require W-2's, 1099's, 1040's, bank statements, paycheck stubs; and access to your credit history and score. They will virtually guarantee your ability to get a mortgage for $s for y years, and can even lock in an interest rate. Yes it will ding your credit score.
The good news is that multiple pulls during a short window isn't bad because they are considered as a single pull, to allow the borrower the ability to shop for a loan
We were also told to contact a mortgage broker, but so far the people
we've been recommended to are direct mortgage lenders.
I'm a bit confused about the whole process. What should we do? How can
we shop around for the best rates? Can we have a broker look into
mortgages with specific companies, or is it our responsibility to do
the footwork there?
A mortgage broker will represent multiple lenders, but they won't represent all lenders. Many people start with their bank or credit union. They know you, and can do some of the pre-approval steps without as much paperwork on your part.
If they don't have a good loan department, or their rates don't seem competitive based on what other places are advertising, some borrowers move on to other lenders or even a broker.
The broker will be able to take your information and get quotes from multiple lenders. In the past there were some problems where brokers steered people towards certain lenders based on the compensation they received from the lender, though recent disclosure laws have limited their ability to hide those fees.
Most (all?) places will have fees related to getting to pre-approval, so you don't want to go through the process too many times. But by starting with who you know, and then broadening your search you should be able to get to the loan approval state quickly.