First and above all, use a Mortgage Company not a Bank. Banks do not have all the loan products that are available on the market and their specialties are CDs credit cards, savings & checking accounts, ... not mortgages. Typically a bank only wants to do a mortgage for people with perfect portfolios. You want to be approved, not turned down.
Even more important is that a bank doesn't carry all the mortgage programs available today. A Mortgage Broker has countless lenders to put your loan through and will therefore get you approved in the loan that is best for you. They will also be able to get you a better interest rate than a Bank can. There are few exceptions to this.
Make sure they are HUD approved!! If they are not you may be getting a loan at a higher interest rate because they are not approved to do FHA mortgages. FHA loans are and have always been one of the best loans availiable. Many brokers are not approved because HUD does a background check and requires that the company has a minimum net worth. It is easy to get a brokers license but it is not easy to to get HUD approved.
Be Ware. Some brokers will say "yes, we can do FHA loans" but reality is they are brokering them out to another HUD approved broker. Guess what that means. More fees for you to pay because no one works for nothing! Simply ask if that company is HUD approved. If they are they are sincere about doing what is right for the borrower and they follow the rules. If they don't, they are fined and they lose their HUD approval.
Make sure the Mortgage Company you use carries all the products. Conventional/Non-Conventional, Conforming and Non-Conforming and that they have many different lenders to choose from. A good Mortgage Broker will have from 40 to 100 different lenders to choose from.
Your Loan officer should have a minimum of 2 years experience as a loan officer. Five years is best but two is very good. There is a lot to learn and it is a very complicated business. Ask your loan officer how long he has been with that company. Sometimes there are legitimate reasons to change companies but if he continuously jumps from company to company it is a red flag. Ask for a different loan officer.
The Company you use should be listed with the Better Business Bureau. Seriously! If they are not, don't use them. In fact, if you like you can call the BBB to see if they have any complaints filed against them.