Gauge your interest in the property and the fairness of the price and make your offer accordingly. However, keep in mind, lower price ranges in the market are very sought after. Someone can always outbid you.
But, one thing to consider when you are purchasing that low is that you may be limited to paying cash only. Many lenders and banks will not provide a finance loan for less than $50,000. I only know of one local lender in my area that will go down to $40,000.
If you are paying cash, you can negotiate and close fast. If you are trying to finance, you may be out of luck.