Mortgage Bankers in your community will provide you with a much higher quality of service and financing options than any "Big Bank." Local Mortgage Bankers have long been the source of excellent financing options for homebuyers. Further, Loan Originators who work at Mortgage Banks are LICENSED whereas Loan Originators who work for the "Big Banks" are only REGISTERED. There's a BIG difference.
Sit down face to face with your Mortgage Banker to be thoroughly prequalified. The Mortgage Banker will review all facets of your loan request to answer your questions with regards to the types of loans and maximum loan amounts you could qualify for.
Consumers have been led to believe---thanks to huge advertising budgets with the BIG BANKS---that they should go to their bank for a mortgage loan. This is the WORST place to get assistance with the BIGGEST PURCHASE of your life! These BIG BANKS are basically BIG CORPORATIONS. You're a number, at best. With a Local Mortgage Banker you will be treated like a friend and a client for life. You can't imagine the high quality of personalized service you will receive from a Mortgage Banker until you try.
As to price---rate and fees---competitive if not better than the BIG BANKS.
You can verify the License of any Licensed Mortgage Loan Originator at nmls.consumeraccess.org
What kind of loan and what kind of house? the government isn't actually the entity that give you the loan, you go to a bank or mortgage lender that takes your application, looks for a loan product that fit your needs and arranges for the loan.
You need to start at the beginning, a review of your finances and needs by a good Realtor would be an excellent way to start.
Lots of those here, including me. Call or email if you'd like some help.