You should meet with a mortgage banker. Bring your last two years tax returns, bank statements showing your assets and your credit rating report from Australia. Do this in person, not over the phone, this way there will be less margin for error. The mortgage banker will also pull up your credit report here in America and then be able to make a determination as to your qualifications, how much you can borrow and the mortgage rate and program options avialable to you.
Once you do this, you can then get a pre-qualification letter from the banker and start sopping for your home. With regard to an attorney, you will need one once you negotiate a deal (usually through a real estate agent like myself) and upon getting your offer accepted, you would put your attorney in touch with the seller's attorney so they could prepare a contract of sale. You do not really need an attorney prior to that and you are not legally obligated in anyway until after you sign that contract with your attorney protecting your best interests. So you have nothing to fear.
Your best bet would be to put 20% down so as to avoid having to pay Private Mortgage Insurance. If you have $250,000 to put down, you would want your purchase price to be no more than $1,250.000.00. On this type of purchase your monthly mortageg payments would be about $6,320.00 per month on a 30 year fixed mortgage assuming you are qualified. You also have to pay real estate taxes and homeowners insurance which would add $750.00 per month bringing your monthly living expense to $7,070.00. In order to qualify for this type of mortgage you would have to show an income of about $300,000.00 per year (this amount can vary from bank to bank).
Given the price range that you are in, you could find a 2 family home and get a rental income to help qualify for the loan if need be and of course help with the monthly payments as you had mentioned.
If I can be of further assistance, please contact me. I can help you find houses in Park Slope to view and also put you in touch with a mortgage banker if you need a recommendation. Good luck!
Mitchell S. Feldman
Madison Estates & Properties, Inc.
Office: (718) 645-1665