Welcome, Tom. . . . .
Do NOT buy from the Craig's list person. As jmiked said, the files are almost certainly not legal copies. They would probably work, but they might be corrupt files; they could conceivably even harbor something that would damage the Kindles OS. Just not worth it.
If you want classics, they're legitimately available via Amazon, manybooks.net, feedbooks.com, and project gutenberg. Those are all legitimate sites and anything you find there is public domain or an authorized version.
Scammers/Pirates will always find a way. . . . .but honest folks should not support them.
As to whether Amazon will do anything about it. . .well, it's kind of not their fight. The rights holders are the ones who should go after these folks. If a book is uploaded for sale at Amazon and they discover it's not an authorized version, they'll pull it and refund the money of anyone who purchased it in good faith. The first time this happened they also removed the title from Kindles but people didn't like that, to put it mildly, so they've said they won't do that any more.
Beyond that, they really don't care what you put on your personal device. They won't convert something that has copy protection if you send it to them to load -- it just won't go through; they don't report you or anything. But removing copy protection from books purchased at Amazon (and via most other legitimate ebook retailers) is against the terms of service. If it's discovered you're doing that, they can terminate your account.
If you want current titles I second Juanny's recommendation (Welcome to you, too!). And there are some sites that will do a sort of price watch for you. Some titles might be available via your local library. Some may be available via the Kindle Owners Lending Library if you're a "Prime" member. But, in short, if it's for sale on Amazon, and someone is offering to get it for you at a lower price, or free, it's probably NOT a legitimate copy -- unless you're talking about an independently published book that may be priced differently in different outlets.
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