If you find a Panasonic and it is fixable at a reasonable cost, buy it. Here's the story of the company written by the manager of the bike shop where I worked at a very long time ago.
Panasonic Bicycles at Yellow Jersey IMHO, it was the one moderately priced bike sold by Schwinn that wasn't a BSO. Panasonic sold to dealers under their own brand name but also slapped "Schwinn Approved) labels on the same bike and then had them sold by Schwinn dealers as the World Tour for about 30% more than the comparable Panasonic. Made in Japan.
You are right that almost all of the bikes donated to places like yours are junk not worth fixing. That's simply because most people buy their bikes from places like Walmart so they are BSOs to start with. When I see a bike that doesn't have a one piece crank and wheels held on by nuts, I lift it up. If the bike is light and not trashed, it probably is worth restoring. Most of my restorations end up well under $100 but I am very choosy about the bikes I restore.
There are those of us who restore bikes as a hobby for the pleasure of the next owner, not for profit. I pass mine on to Scouts and Scout leaders who do cycling merit badge. The OP is in this category.