The above link takes a look at how to pick the right lens.
Fixed focal length lenses offer a very traditional way of shooting. Before zoom lenses existed, this was of course the only way to shoot and as such a lot of the cinematic look that we are used to seeing on film today was established by early DPs using primes.
Today, primes are used as much as ever on professional film sets, and I highly recommend them as part of your kit, especially if you're going after the film look.
The main advantages of a prime lens are:
Although zooms are less traditional on a film set than prime lenses, they are certainly still widely used on productions of all sizes. Many of my favorite directors and DPs use (or have used) zooms, and for good reason. They offer a number of advantages over primes including: