There are many different kinds of oil colours on the market to find. Some are high quality and very expensive but, believe me that high quality is all worth to buy. I use Winsor & Newton Artists and Rembrandt Oil Colours but there are many other good ones such as Da Vinci Artists or Gamblin.
When you buy brushes it’s also worth to pay a little bit more since very cheep brushes tend to brake in the brush and leaves particles on the canvas. Purchase some hard and some very soft brushes which will help you achieve the results you want and need.
Don't be afraid to invest in many different sizes and shapes, its all worth it and the big and expensive brushes can hold out for years. My favorite brush brand at this time are the Da Vinci Nova. Try out which brushes you like the most. Some of my brushes are very big and some are the smallest you can buy. Flat brushes are the ones I tend to I use most.
Easel, Oil painting Palette (wooden, plastic or paper palette), Storage box, Brush Vase, Turpentine, high % Soap to clean brushes, Drying Linseed Oil and finally Household roll of paper to clean brushes when you paint.
There are many different canvases to choose from. I use stretched linen canvas for my oil paintings. The ready-stretched canvases available to buy in art stores would limit me too much. However, you can find oval, 3D or traditional stretched canvas which are ready-stretched.
It's up to you, purchase already stretched canvas or learn how to stretch the canvas to a wooden frame yourself. Read my Article about how to Stretch your own Canvas »
Canvas papers and canvas boards with hardboard are also an option but I wouldn’t use it myself for my clients, because I’m selling high quality pet portraits and it’s very important the canvas is stretched, but for learning its great!