If a lens says f/2.8 only, that means the widest aperture it can have is f/2.8 (so it won't go any lower than that)
Of course you can do incremental increase from f/2.8, f/4, f/5.6,... to f/16 or f/22 for example.
When a zoom lens says f/2.8 (eg. 17-35mm f/2.8), that means it can always perform at f/2.8 no matter what focal length you use. Although some lens may have an exception, like Tamron 90mm 2.8 for example. It can only do a constant 2.8 if you are within a certain range from the object (3m or so), but when you do a very close macro, its minimum value will change into f/5.6
But basically, when a zoom says f/2.8 only, that means it can do f/2.8 all the time (which is really what you want in a lens).
But if a lens says, eg: 70-300mm f/4-5.6, that means that lens will have the minimum aperture value of either f/4 or it can be f/5.6 depending on the focal length you choose. So sometimes the aperture won't go any lower than f/5.6 when you change focal length.
Basically what you want is the focal length(s) to be as low as possible (or constant), but this is reserved mainly for pro-grade lens (more $$$ compared to non-constant ones).
So when buying zoom lens, consider the f value it offers, because the range it covers might sound good, but it can actually be a painfully slow lens.
Maybe if you are shooting mostly in bright daylight, it's not much of a problem to have slower lens, but when it's a tad cloudy or during late afternoon, you might find that the non-constant one will be too slow to take a sharp shot (because you need to use slower shutter speed), and it that kind of situation, you will want a fast lens (so that's when the f/2.8 will show one of the benefits)
Basically, lens aperture doesn't depend on the camera, but on the lens itself.
If you don't have the budget to get a constant aperture zoom, but you want a fast lens, other option is to have a couple of fast primes, since they are generally cheaper. Although that means you have to change lenses to get the focal length you want. But for film, I think you'll be fine if you have 24mm and 50mm primes for a start. Used ones are not that expensive.
I hope that helps.