A very complicated question, to which there are just as many complicated answers!
By far the largest majority of film users I know, use 35mm cameras, but there is a hardcore of medium format film users fast catching up.
We as film users are by now quite comfortable with the type of format and film we have been using, but to a newcomer to photography, it can be a daunting decision to make. First and foremost is the price and what your budget will allow; I would look at spending at least £50 to £100 on your first film camera, examples of which I recommend are the Olympus OM1 slr, Canon AE1 and Pentax ME Super. These are very good value for money right now and will serve you really well, being quite simple to use, and having the benefit of autoexposure if and when you need it.
There are others as well, much cheaper, such as the Russian line up, including the Zenit E, Fed and Zorki, but these can be quirky, so I wouldn’t recommend them to a beginner!
If however, you are really set on medium format, then you cannot go far wrong with the Yashicamat and Mamiyaflex range of cameras; there is also the Rolleiflex range, but these are very much more expensive, although if you can afford one, I heartily recommend you go for it; prices for Rolleiflex cameras starts around the £300 mark and upwards.
You will find that using medium format is quite slow process; there is the composition, exposure etc, not to mention the transposed image in the Yashicamat cameras (ie left and right are reversed in the viewfinder), but it as all very good, as it teaches you what photography is all about, how to compose a shot, judgement of lighting conditions etc., something a fully automatic camera will not allow.
And then of course there is the quality, although as a beginner, you will not be too worried about that, seeking to shoot photos with correct exposure and composition first and foremost.
The state of your pocket also comes into it again, as medium format film is in general, a little more expensive to process compared to 35mm; it is also higher in price to buy as film.
In closing, I would suggest a radical departure from the above for newcomers — start out with a cheapo digital camera! Yes, I mean it! The beauty of using a digital camera in the initial stages, is that it is very forgiving as a tool; you can shoot away to your heart’s content, review your shots then and there, and learn from your mistakes.
What digital camera do I recommend? I myself have a 2 megapixel Nikon digicam, very very basic, but who cares? It allows me to quickly take a prospective shot, review it, and shoot it again with my film camera if all is ok.
There is obviously far, far more to the subject of medium format against 35mm, something which we will go back to many a time here, but for this time, I think the information above is sufficient to allow you to decide which way you want to go. This much is true; you will have taken your first steps in a superb hobby, that you can take as far as you want, either as a profession, business or just a hobby!