Efficient screening

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There are many many web sites offering access to foreclosure and related data. Most allow free 7 day trials, then cost ~10/week. Most appear to contain very similar data.

So I signed up for one of them, and it presents me with a very large list - over 3000 listings - mainly single family home foreclosures. (BTW, I live in a midwestern city with a population somewhat over 2 million).

The site helpfully shows a listing price, and, for most listings, an estimate value from Zillow, for whatever that's worth. When I scan the list for apparent mismatches (i.e. house listed for $200K, Zillow estimate of $300K), then look closer at Zillow, I find as often as not that Zillow's estimate is likely off, either because there are few comps close to the house in question, or because there is a significant difference between those comps and the house in question (i.e. the comps are part of a new subdivision, the target house is much older).

What is the best way to get from this 3000+ house database to a manageable number of viable prospects that I can spend more time evaluating (including, eventually, a drive by)?

Also, for houses that are foreclosures, I assume they are mostly bank owned, correct? How much negotiating room will there typically be on these houses? None? 5%, 10%?