Unlike the painter, a photographer has little control over color. We can manipulate colors with lighting and filters but overall colors we photograph are subject to the film we use, none of which are true reproductions. Some come close, some are dull or seemed washed out, while others are vivid or even surreal.
True, in this age of scanners and photo-manipulating software, there is a great deal of control over color, but I'm talking processed film here before it's scanned into a computer. Every film is different. Each will give the finished product, whether negative or transparency, a different degree of color. This is true even within the same brands of film and even within batches of the same type film within a brand.
For instance, Kodak films are generally more realistic while Fuji films are more color saturated. But even within Kodak, their Kodachrome will give different colors than their Elite Chrome, just as Fuji Velvia will gives different colors than Fuji Sensia.
I'm not an expert on film and don't pretend to be. But as an amateur photographer I know different films will give different results. The various brands of film and the types within those brands do a fairly good job of keeping their color constantly the same.
As to the difference between slide and print film concerning color, slide film is less tolerant. A third stop difference in exposure can make a great difference in slide film, while that same difference on print film may take a full stop or more. However, their are guidelines for slide film. Slides you have mounted are the pictures you took, while with print film there are no guidelines and those who print out your negatives manipulate them to look what they believe to be best and not necessarily what is imprinted on your negative.
Besides color, one must also consider film speed. Faster films, those with low ISO/ASA numbers, have a finer grain and thus higher quality, especially when blown up to larger than 8x10 prints. If you're having normal prints made from negative film, speed is less important, you'll see little difference. However, if you are using slide film and viewing those slides on a big screen you'll see the grain of faster films. My general rule is to use only 200 ISO print films or slower for most of your negative photography, using 400 or 800 only in situations where a tripod is not practical. For slide film use only 100 ISO or slower, using 200 or 400 ISO in special low light or fast moving situations.
Another consideration is the difference between pro and amateur films. The main and really only difference between most pro and consumer films is consistency from roll to roll and batch to batch where a professional photographer absolutely needs to have his colors match. Otherwise, they are pretty much the same. Fuji's consumer 100 ISO film will make photos as good as their pro 100 ISO, as will Kodak's, Konica's and others. However, there are pro films that don't have a consumer/amateur counterpart, such as Fuji's Velvia 50 ISO pro film. If you want to shoot with something like that you'll have to buy professional film, but otherwise the increased cost of professional films over consumer counterparts are not necessary. I guarantee you won't be able to see a difference.
There's only one real rule of thumb. Try as many different types of film as you can and then stick with the brand and type that best gives you the results you want.
Films I primarily use are: Fuji Velvia 50, Fuji Velvia 100, Kodak Ektachrome 100 VS, Fuji Sensia 100, and Fuji Sensia 400 slide films; Agfa Ultra 100, Konica Impressa 50, Konica Centuria 400, and Fuji Superia X-tra 800 print films; and Agfa Scala 200 Black&White slide film.
For digital see Media Cards, also called digital film.