In your lifetime of photography as a hobby, you cannot go wrong if you choose either Canon or Nikon as the equipment you will use. I would think twice about using any other brand of camera gear.
You say "new" glass that can be used on older camera bodies, but most "new" lenses are designed for use on a DSLR (AF-S lenses, or lenses with a computer chip) might not be fully compatible with a MF 35mm film camera body like you list as needed for your class.
I know next to nothing about Canon (as a Nikon shooter for 40 years), but for the 3 (FM / FM2 / FM10) different specific Nikon 35mm film bodies you mention, ALL THREE are MANUAL FOCUS cameras. And in the digital world, they, and their MF lenses - note that I said in a digital world, are basically good for paperweights unless you like to be limited to manual focus lenses. VERY good quality glass is available in a Nikon MF lens, but it will always be a MF lens.
For example. the FM2 is a VERY NICE film camera (better than the other two you list), as film cameras go, but, to answer your question, unless you wish to live in a world of manual focus lenses, the lenses you will use on the cameras on your list for class WILL work on a Nikon DSLR (other than D40 / D40x / D60 / D90 / D3000), but as a MANUAL FOCUS lens ONLY. Also may cause you to have metering issues...
But I would suggest you NOT USE ANY of the three Nikon bodies you mention -
Like the post above that suggests an N80 body, I would also add N90 / N90S (LOOK OUT for the worn coating on the back of these, indicates a much used camera), maybe N6006 to that list - all are VERY NICE AF cameras (if they want you to MF you can always turn the AF to off), and the "AF" or "AF-D" lenses you will use on these camera bodies are fully compatible with, and will work VERY WELL on any Nikon DSLR that contains a focusing motor.
ALSO - if you need to use film to go to class, I would suggest you buy a used camera that fits the criteria (should be able to get a body + lens for way less than $100.00 - in this forum, on CL,
eBay, local pawn shop, or most any used camera store found in larger towns - I could go out in Metro Atlanta TOMORROW, and find a NICE AF 35mm film body, a NIKON, for less than $40.00 for the body only, and probably a body and lens for under $100, the local stores that sell "used" are LOADED with them), then sell it later and go digital - IF you want to go digital. That would be your choice.
The MF film camera you use in class will ALWAYS work very well as a MF film camera. But an AF camera will also have lenses you can use for the rest of your life on your DSLR's.
I have seen TONS of listings on CL where someone going to one of those film classes went to a high-end camera store, paid hundreds of dollars for a 35mm film camera, now trying to recover their costs because they chose to go digital after the class, when same camera was always plentiful on CL, pawn shops, used camera stores - for cheap.
ANY MF or AF film camera will take a nice photo as you learn more how to use it. so try all of the camera bodies that fit your criteria, see what fits and feels best in your hands and choose one of them for the class that fits your needs best.
Then when your class is completed, you can decide if you are going to keep it, or go digital like you indicate you will possibly want to do. If you paid $100 for it you can likely recover most or all of your costs to buy it, if you paid higher prices for it from full price retailers = good luck!
If you buy AF gear you can keep the lenses, worst you are out is cost of a film body, and AF film bodies DO have somewhat better resale value than MF film bodies.
In the long run going digital will cost you more than film for the equipment (at first), MUCH LESS for the image processing than film (after gear had been purchased) - but which way you choose to go, should be YOUR choice after you complete the class.
For the money those classes cost - I cannot believe that they do not teach digital and "on PC" post processing of the digital image... (seems kinda like someone going to school to be a mechanic, spending a TON of money, to learn how to repair a Model T...)
You might want to stay in the film world, or maybe go digital, you never know, but until you DO know, I just don't want to see you sink lot$ of $$ into equipment you may never recover what you paid for it after the class is over.
Hope you take this for how it was intended.
Choose well, buy carefully, pay "thriftily" ...
BEST OF LUCK for your lifetime of happy photographing!