Always remember that the nicest camera on the shelf is useless when you don't have the money to pay for film and processing.
So, with a limited budget I wouldn't go for a Leica. These cameras have addictive and seductive properties and you will soon be spending much more money on them than originally intended. Don't ask me how I know
With a budget of 1000 $ I would go for a nice Olympus OM-2 and two or three favorite lenses and use the rest for film supplies, maybe even a basic set for film development (50$) and a good entry level film scanner (300$). IMO nowadays it is more important than ever to be in control of your workflow and honestly, for me it is half the fun of the whole thing.
Compared to SLRs, rangefinder cameras like the Leica M are quite a bit more expensive and I would suggest that you give them a try at a later point in time, when you are certain that you really want to stick with film and are ready to explore a different shooting style.
If you decide for MF, a decent post-war Rolleiflex in good condition is a reasonable choice. Just be aware that the waist level finder is not to everybody's liking and you should make sure that you will get along with the limitation of one focal length. If not, a more flexible system camera like a Bronica SQA could be the better alternative.