These supplies are only a suggestion. I'm constantly trying different palette combinations, different surfaces and new brushes.

Palette: Generally I use a split primary system with other hues used as circumstance requires. That means:
Cadmium Yellow Light
Cadmium Yellow Medium
Cadmium Red Light
Alizarine Crimsom
Ultramarine Blue
Pthalo Blue, Cerulean Blue, Severes Blue (one of these)

Then I throw in when needed...but not always:
Viridian--when it looks like I will need a cool green....or, with Alizarin Crimson, to make a warm or cool ‘black’.
Burnt Sienna--this is showing up a lot and may be a ‘use it all the time’ hue.
Sap Green--for those transparent greens that are often in the shade outdoors.
Cadmium Orange--when I get tired of mixing orange.
Black--usually indoors.
Quinacrodone Red--replaces both Cad Red and Aliz Crimson.
Burnt Umber or Raw Umber--for cooling and muting certain hues.
Cadmium Yellow Deep--usually just outdoors instead of Cad Orange.
Titanium White

Brushes
Robert Simmons
Windsor and Newton These brushes are growing on me and can be used for water soluble oils and traditional oils. A nice synthetic brush.

Painting Surfaces
Canvas and linen mounted on masonite, gatorboard, or stretched. I also use gessoed masonite and gessoed Bainbridge Board (Utrecht) for quick studies. The Bainbridge Board is used with water soluble oils (see below). Raymar and SourceTek are also good boards that I'm using more frequently.

Miscellaneous
Gamsol for a solvent.
If I use a medium it is either a Walnut medium from Graham or Galkyd Lite.
Sketchbook with pen and grey scale markers. See ‘Marker Book’.
A comfortable camp stool, paper towels, palette knife, plastic bags.

Painting With Water Soluble Oils

Water soluble oils are nice for travel. I’ve used them in France, Mexico, Jamaica, and Canada. With my small pochade I can sit in coffee house and paint with a glass of water. The water is only for an occasional cleaning of the brush...and it may never get used. I paint with water soluble linseed oil and often just dip into the linseed and wipe with a towel to clean. I try and keep water off the painting surface and out of the paint and brushes. As linseed oil is my only thinner, I like painting on the gessoed Bainbridge Board as its absorbent quality keeps the painting surface from getting too slippery. I will often pre-tone the board so I have a dry, but toned, surface to paint on.