Painting in class
First, if you are coming to one of my live classes, you don't need any of this. I supply everything you need to paint in class.
Painting on your own
To start painting Bob Ross style on your own, you need some specific paint brushes, his unique palette knife and mostly firm oil paints. The colors that are used for highlights (Yellows) are made to a thinner constancy for easier mixing and application.
If you watch his very first tv show he talks about the importance of limiting the number of colors used to limit costs and to simplify painting. At that time he was only using 8 colors.
The concept of limited palette is not new. Monet painted with just three colors, a warm and cool of each one plus black and white.