If your budget is extremely limited you have other options besides a new DSLR or a used film camera. You can also find used digital cameras that are 2-3 generations older than the current models for very modest prices. You don't need an SLR or DSLR to start learning, either. A good used bridge camera or compact that has the ability to manually control shutter speed, aperture, and sensitivity (ISO) will allow you to get started learning the basics of exposure, composition, and post-processing (much of which can carry over to the darkroom - almost everything we do in digital post-processing has a corresponding antecedent in the chemical darkroom).

Even if you decide you want to ultimately shoot with film, shooting with a slightly older used digital camera is a faster and more economical way to learn many of the fundamentals of photography, including exposure, composition, technique, and how using different focal lengths, apertures, shutter times, etc. will affect the resulting image than starting out with a film camera would be. This is particularly the case when you're not sure if any problems you might see in your earliest images are the result of user error or of camera malfunction.

Many of us grizzled old-timers like to boast about how we started with film in the era before autofocus existed and how it forced us to learn how to be real photographers.¹ But the reason we did so was because it was the only way to start back then.

Now that you have a choice, though, starting with film is probably not the best way to get where you want to go.

• The overwhelming advantage of digital is that it allows one to experiment and learn without the per-shot expense of film. Your initial cost to start is less with film, but by the time you've shot your first 1,000 frames the cost of film and developing will have overtaken the cost of an entry level DSLR. By the time you've shot your first 10,000 frames² just the film and processing could have bought a nice lower end pro-level digital system.
• There's also much to be said about the instant feedback of viewing a histogram on the back of the camera immediately following the shot. In the film era some of the best photographers in the world would use a polaroid back to test their lighting setup before loading the film and shooting.
• Digital allows you to set the ISO and white balance of each shot individually, just as a century ago with the use of sheet negatives. Roll film, on the other hand, locks you into a specific sensitivity and color balance for an entire roll of film.
• While there is much to be said about the lessons learned from processing your own B&W film in the darkroom there are just as many lessons that can be learned from developing your raw digital files on the desktop. You can also learn a lot about exposure, contrast, white balance and color, composition, etc. by processing your photos critically with the digital equivalent of a darkroom - your computer.
• Digital cameras record information with each frame that tells you what aperture, shutter speed, ISO, metering pattern, AF point, etc. you used. This is extremely helpful when reviewing your images to see what did and, perhaps more importantly, what did not work. In the film days a student would need to stop and write all of those things down for each shot.

¹ The ranks of those who learned in the era before auto exposure are much thinner than they were just a decade or so ago. There are very few, if any, shooters left who started before most cameras had built-in light meters!
² Henri Cartier-Bresson is oft-quoted as having said, "Your first 10,000 frames are always your worst." He was perhaps the greatest street photographer of the 20th Century and is certainly one of if not the most well-known. In photographic circles, the initials HCB are enough to positively identify him.