The answer to your basic question is, "It Depends".
There are what I like to call the Three Pillars of Lending: Credit, Income and Assets (CIA, for short).
Credit: With a 770 credit score you should be able to get almost any loan out there (assuming it is a mortgage-related credit report--many people get other types of reports and tell me they have , for example, a 936-credit score, which does not exist in the mortgage industry).
Income--You ask about this pillar. It really is not a question of how low your income is, but what is your "debt ratio". Take your current credit report -type payments (car, credit cards, etc.--versus, life insurance premiums, food, utilities, etc) AND your new house payment (including principal, interest, homeowners insurance, real estate taxes, homeowner association dues, etc.) and divide the total by your monthly income. This is your debt ratio. For conventional loans, you should be below 45%, or have positive compensating factors to get to 50% exception. FHA, they want 55% or lower. I have helped people with as little as $800 in monthly income get into the home of their dreams...
Assets--This is determining if you have enough verifiable cash or other "liquid assets" to make the downpayment on the home (you indicate $18,000 or about 23%, so no mortgage insurance), plus pay for any uncovered closing costs and prepaid amounts (real estate taxes, homeowners insurance, interest).
So, probably more than you wanted to know, but all three pillars matter.
Give me a shout if you wish further information and a good lender to work with in the Maricaopa area.