I use a basic split primary palette with additional colours for speed and vibrancy. I have a variety of brands in my selection, and would recommend any of them for a serious beginner in watercolor. This includes Daniel Smith, Schmincke, Old Holland, Daler Rowney, Winsor and Newton, Sennelier, Maimeri Blu and M. Graham. The Chinese manufacturers are also contenders for quality at rock-bottom prices, and I have tried and can recommend Paul Rubens, Meeden and MeiLiang. I also like the handmade paints from Italy sold by A. Gallo.
Basic Core Palette
Lemon Yellow
Cadmium Yellow
Ultramarine Blue
Phthalo Blue or Winsor Blue
Sap Green
Alizarin Crimson
Cadmium Red
Yellow Ochre
Burnt Sienna
Burnt Umber
Lamp Black
Chinese White
Useful Additional Colours
Naples Yellow or Buff Titanium
Cadmium Orange
Quinacridone Gold
Cobalt Blue or Indanthrene Blue
Hookers Green
Olive Green
Permanent Rose or Quinacridone Rose
Permanent Magenta
Winsor Violet or Dioxazine Violet
Indigo or Paynes Grey
Raw Umber
Raw Sienna
Olive Green