There are already some good suggestions here (as well as the usual misinformation). As I read this thread, both AY (Andre) and Luc posit valid points. And I will absolutely concur: a Leica rangefinder will NOT by itself make anyone a better photographer, in film or digital. If this is about acquiring status symbols there is no point in the discussion.
I will take the OP's original requests (and not the inevitable and somewhat ridiculous film v. digital debate) as the basis for my suggestions.
The OP would like to:
1) Learn film photography.
2) Become proficient at composition.
Re:
1):
Learning film photography requires understanding and then controlling/manipulating the relationships between film, exposure, and chemistry, whether in b&w or color, otherwise too many variables will constantly affect the results. Given that, a good home or rented darkroom or a high-quality developing lab (what milosz already stated) are requirements. Otherwise, one simply cannot control the various film/developer/temperature/water/etc. etc. variables.
I believe starting in b&w is easier (technically, color film is very easy to develop, but there are other issues, such as paper + color enlarger, etc.). It also eliminates the color variable in composition, if one can learn to visualize.
Choose one film, choose one developer, choose one exposure system. And work from that, at least for the first 6 months.
I.E.: Kodak Tri-X; Kodak D-76; Zone System exposure. This is only one of many basic aggregations, but it is time-proven.
The Ansel Adams (many: "Basic Techniques..." or the film and printing "Zone System" books); White/Zakia/Lorenz ("The New Zone System Manual"); Picker ("Zone VI Workshop"); and Stone ("Darkroom Dynamics") are all good starting points.
Learn to understand the balance between film characteristics (toe, mid-range, heel); developer (time and temp.) and exposure system.
Re:
2):
This is trickier. What is "good" composition? One needs to practice, practice, practice, and look (study), look (study), look (study) at a lot of previous photography.
No camera per se will make one a better composer, and much depends on one's own vision, but in my opinion if one doesn't develop a relationship with the viewfinder any exercise will be almost fruitless. Given the OP's desires, I would suggest of course studying the great street photgraphers, some already mentioned here (since the OP is shooting in 35 mm) and ensuring that his camera has a good, luminous, 100% viewfinder. But, mainly, try different approaches (simple or complex division of field, no horizon, field edge information, etc.). Study the great painters as well.
That said, however, the best exercises in developing photographic composition skills most quickly often come from using a view camera. The camera is stable, on a tripod. Precision adjustments are possible. The images are often static, such as landscapes. The image on the ground glass is very large but is also upside down and reversed; therefore the visual concentration required to compose is both easier to see (esp. edge of frame) but visual elasticity is also required, until composition becomes second nature. And if one then thinks view camera photographers can't shoot in the street, just look at Stephen Shore, Max Yavno, Walker Evans, Paul Strand, etc.
Whatever you do, don't use the zoom lens.
For both film practice and composition, yes, a course is a very good option, if the teacher is good. In any case, learning will require lots of practice, patience, and precision.