35mm photography is the most common film size as it is what we have used for many decades. Before that there were larger formats, but the equipment tended to be very heavy, slow to use and required a lot of skill and concentration. Oscar Barnack famously helped develop the first 35mm camera and the accompanying film to use with it. Now, the film was already available in that size, but it was used for filming movies. He had the idea of flipping it on its side essentially making the usable area larger and having it run side to side instead of up and down. This was such a great idea and it soon helped to pave the way for Leica rangefinder cameras which were diminutive versus what came before them. A better viewfinder system was developed over time and the mirrored cameras were also developed around that time.
I don't want to go on a rant about the profoundness of this and how the SLR came about and changed things once again, but most importantly the 35mm film format stuck and is still being used to this day. What we use now is made of stronger materials than the original, but essentially they are the same thing. Over time they were able to come with different kinds of film that would react to light differently. At first they were all meant for black and white images, but soon the technology was made to have them produce color images. Once again a lot of evolutions of this happened and several large manufacturers jumped in to claim their own unique recipes. As they say competition drives creativity and today we have many film types to choose from, although not as many as in the golden age of film. Nonetheless today you can shoot in color, black and white, slide film and all kinds of other films. They remain costly as they require very special machines and processes to make them. And they have been standardized over the years to generally only have 24 or 36 frames in them. There are other variations, but these are the standard.
But, as these were adopted as the standard it was easy for manufacturers to develop cameras to work with them as the standard was a global standard that hasn't really changed. Today you can find a lot of manufacturers with decades of film camera releases. All your favorite digital camera brands have a long history of making film cameras as well.
Although new film cameras are hardly being released nowadays we have thousands of used cameras out there in the wild to choose from. Your parents might even have one laying around. Many film cameras are still functioning today and will for many years to come. Service them, treat them well and they could easily out last you.
I have shot with larger formats, but 35mm is my go to for my daily film photography. Generally they keep the camera small and there are tons of options out there.
35mm is here to stay!