Stories of great scores at thrift stores are by far the exception. You might stop at those 9 stores 20 times each (and 50 garage sales) and still never find anything good...or you might get lucky on your next visit.
And with the improved economy of the last 3-4 years, and the renewed interest in vinyl, demand for used audio gear has skyrocketed...making gear that much harder to find.
Also, the proliferation of ebay and similar venues has made it very easy for even those with no audio knowledge to value (and often overvalue) the stuff they are looking to get rid of. This too makes it harder to find good stuff cheap.
You are right to consider later-era gear...demand for it has not yet hit the levels seen for "golden age" gear (late 60's thru early 80's). While the proliferation of IC devices in the 80's can make this gear harder to repair, there were plenty of pretty good integrated amps, power amps, tuners and receivers still being made by the big manufacturers in the 80's (Pioneer, Kenwood, Yamaha, etc).
My curiosity was piqued, so I took a look at CL in Houston. There is a Pioneer SX-737 for $125, claimed to be in good operating condition. That would be a good start for a budget system. There is also a pair of little Boston CR6's for $50. I assume both of these items could be bought for at least a bit below the asking price. So for maybe $150 you would have system that I would have loved to own when I was younger. Add a decent small, used subwoofer later and you might have a system you'll keep for many years. In any case, good luck.