Shoot as many films as you like. If you enjoy that, then you should.
It will benefit you in different ways though if you concentrate on fewer films, and work carefully and closely with your lab on how to get the most of your materials.
Annie Leibovitz probably did print her early Rolling Stone work. If not, they were probably printed with her involvement. And the magazine's process then most likely was based on what were essentially photographs taken of the prints that were made conventionally by her or with her involvement.
Or if she shot slide material, the slides themselves were essentially photographed.
In most cases, in a blind test, it is just about impossible to identify categorically what film was used in a particular situation if there is an intermediary that is either digital in nature or if a photograph has been reproduced for publication. The intermediate steps add their own characteristics and get in the way.
Well, I can almost always spot a kodachrome
Don't worry I'm thinning out my favorites... Slowly...