I've had a Nikon FM for 25 years and I love that thing. Remember there is no autofocus or auto exposure. I learned a lot about composing pictures with that camera.
Does the Nikon FM have through the lens metering?
We got our daughter a Nikon FM for high school graduation in 1982 and it's still going strong. She bought a second matching body a couple of years ago. You're right, a simple camera will teach what you need to know.
I have a couple of Pentax ME bodies myself which date to about 1978 and they too are still clicking, so to speak. I would advise buying from a reputable camera dealer rather than on Ebay as there a lot of things that *could* be wrong with a used camera. Even then one should be sure that "return" privileges are extended in case of problems.
My daughter got a zoom lens smashed in airline baggage, so I went out to get a replacement from one of the local big stores. The salesman told me that lens was "no longer available", but the manager, a sort of Middle Eastern looking fellow, overheard and sensed a sale slipping away. In nothing flat he grabbed a new camera out of the case and popped the lens off and sold it to me at a decent price. That's the kind of place to look for older stuff.