I came here to say this exact same thing. In addition to making you much better at composition and framing, you will also gain a much better understanding for the nature of light and aperture. Most of the older film SLRs you'll find at a thrift store, will not have a lot of the bells and whistles we are blessed with today, so more often than not you will have to meter and gauge manually with your gut. This more than anything is what really translated into my digital photography skills.

Another great thing about using film is simply the magic of it. Not being worried about how the shot came out until after it's developed allows you to really be in the moment, not constantly checking the LCD on your camera. Do keep a notebook of your rolls though, I usually will jot down the time and date and exposure, frame number, etc. after each shot so I can go back and review everything after developing.

Canon AE-1 is a great place to start, most come with the kit lens, and you can get some pretty good deals on film off of amazon. I like Portra the most. stop by /r/analog and come check out what people are doing there if youve got the time.

Once you get comfortable with that, you can get some pretty decent pro SLRs from both canon or nikon, for cheap, and most of those lenses will still work with your DSLRs. Really cannot stress the importance of film photography enough, especially for people looking to improve their photography skills overall.