Walnut oil is supposed to dry with a harder paint coat than Safflower oil, but you don't have to use walnut oil. The mediums that are with the same brand of paint you use are fine. Also, I use Winsor Newton Artisan mediums, but I don't use Winsor Newton Artisan paint. I use several other brands of water mixable paints. I like Artisan thinner and their stand oil mixed together, too. Hope this helps. Happy Painting!
Dayle