Oil Paints
Oil paint is what many of the great artists used and use. It takes a while to dry, so you can manipulate it and work with it longer which gives it more flexibility. Oil paint is used on canvas.
For the Beginner
If you are just starting with oil paint, or especially any paint at all, you will need to start with a beginner set of oil paints. The Gamlin Oil Paint set is a great beginner set.
Gamblin Basic Oil Paint Set basic oil paint set

If this is a little expensive for you, you can choose a cheaper alternative such as Daler Rowney Introduction to Georgian Oil Paints.
More Advanced
If you are more advanced, you may want to purchase larger tubes of oil paint separately to get more paint of just the colors you want. Georgian Oils are very good.
Mona Lisa Odorless Paint Thinner 8 oz. bottle
Or you can use a turpenoid, which is like turpentine but is less harmful, such as: