My experience with lenders (lately) is that if you can show--beyond a shadow of a doubt--that you DO NOT NEED a loan, they will gladly make a loan for you. So I would say that you would qualify for a purchase in the $130K range. But you will have to put your $70,000 down, and borrow the other $60,000. It will be good to have 55% equity, so you won't need PMI (private mortgage insurance).
Then of course the house will need to appraise, and you will need a cushion for taxes and insurance.
If you only want to put down a minimum amount, figure $15,000 down on a purchase of $75,000, in which you borrow $60,000.
$75,000 may not buy a huge home in West Springfield, but the numbers do work.
If you find a smallish 2 family in which you could live in one side and rent the other, about 80% of the income you can generate from the rental will be considered income, so that might raise your personal income to 30K or so, and that will change all the numbers, with that income you might be able to borrow $90,000, and if put down $25,000 or so the purchase price could be $115,000.