Which type of company are you talking about? There are mortgage brokers and mortgage lenders. All it takes to start a mortgage brokerage is several years of experience in the business, working for a mortgage broker or a mortgage lender and learning the business. Then you may need a license to operate a mortgage brokerage in your state. You need to find a good location to rent, a place that gets high traffic/exposure. You need the furniture and the phone and computer systems to support the operation. You need a presence on the web and a reliable support service for that. And while you were working in the business, you should have been networking with the various mortgage bankers, so that you have immediate availability to their product - mortgage money. I would say $100k ought to be enough for start-up, but you can expect monthly operating costs to be $5,000 or more. Will you be generating enough points off of the mortgages you broker to pay your expenses and turn a profit? That's something you'd better know ahead of time.
A mortgage lender is a fancy name for a bank. You need millions to start a bank.