There seems to be more to your question than appears at first glance. If you are asking what makes a home a candidate for a short sale, it is that the current fair market value is less than what is owed on the property.
If you are speaking of buying through a short sale, then other questions must be answered. Are you wanting to buy to live in the property?
Are you going to wholesale the properties, retail them, or buy and hold? This can make a difference.
If you are a wholesaler, in what areas do your buyers want to purchase? Retailer, are properties moving in the area? Buy and Hold, is it a good rental area? Your exit strategy can have a lot to do with the area you purchase in.
The price you pay can also vary, depending on your exit strategy. If you are wholesaling, your target price should be below 70% ARV - repair costs - profit.
If you are retailing, you might be willing to pay a higher price because you will be attempting to sell for ARV, but also take into consideration profit, closing costs, holding costs and the market trend. If the market is trending downward, meaning the prices are still dropping, you have to take that into consideration, when making an offer.
If you are buying and holding, then the target to shoot for is the 2% rule. This means that you can get 2% of the purchase price in rent each month. If you can get $1000 in rent, then you would want to spend no more than $50,000. This is an oversimplified explanation, and is not a hard and fast rule, but a good guide.
Hope this answered your questions.