I had both a Nikon FM and an FM2 at one point. They are pretty much the cream of the crop for manual SLRs.
However, I started with a Pentax K1000. Do an
ebay search on 'Pentax K1000'. Look through those auctions. Don't be impressed with "includes 5 lenses", but when you look at the lenses, they are all crappy "Focal" lenses from the 70s. There are some good aftermarket lenses, but for the most part, the lens you're interested in is a Pentax 50mm f/2 or f/1.7 or f/1.4. The cheap bag is not worth much either.
Are you forbidden from having any automatic features, or do you just have to make sure you have manual in addition to the manual features?
Other options: Minolta SRTxxx (any of them) Minolta X-370, Minolta X-700, Olympus OM1n, Canon Ftb.
You could also search for "student camera"
Here's another option: Buy the Canon EOS 620 I have for sale in the Buy & Sell forum, and the 35-70 zoom lens. It has full manual control, can focus either automatically or manually, but it also has full automatic and partially automatic control for when you're "off duty" and just want to take some snapshots. It is a pro grade camera, and the price is reasonable. Another perk is that if you go digital later, you can still use this lens. I'll give you the camera & lens for $150 shipped, if you're in the continental USA.
If you are forbidden from having any automatic features, never mind. But if you can have them and they will trust you not to use them, it is another story.