1 ACRYLIC PAINT SURFACE:
8" x 10" or 9" x 12" White Canvas (the type that has primed (coated white) canvas stretched over a wooden frame & stapled to the wood on the back is my preferred type - you'll also be able to find some that are stapled to the side of the wood frame.  (Other options listed below would work well, too.)

Options instead of the Stretched Canvas listed above:
Canvas Panel or Canvas Board  (not as thick as stretched canvas & feels more solid like the canvas is mounted/glued to a stiff cardboard)
OR a piece of Acrylic Canvas Paper that usually comes in a pad of multiple sheets.

ACRYLIC PAINTS:   (not tempera, not watercolor, not oil)
I suggest as least 1 ounce of several different colors (Basics include Blue, Red, Yellow, White & Black plus Green, Orange, Purple & Brown if possible although your child may not choose to use all of the colors.)  Thicker Acrylic Paints in Tubes are best for this project. 
 Try to avoid using plastic bottles of thin paints that sound watery when shaken.  

PAPER PLATE to use as a paint palette. (Optional to use a plastic paint palette instead or even a disposable pie tin)

ACRYLIC PAINT BRUSHES in a variety of sizes.  Include large, medium and small size ROUGH Flat Brushes (looks like a square on the tip but bristles are rough and a little prickly to the touch.  Also include a couple of very small SMOOTH Acrylic Brushes (1 very small Round brush like a pencil tip shape and 1 slender Flat Square Shape)

WATER in a metal can, plastic cup or glass jar.

PAPER TOWELS

Please also see the attached photo to see examples of both rough and smooth acrylic brushes.  Please avoid brushes that have bristles that bend when wet - those are for watercolor instead of acrylic.  Firm brushes are best for acrylic.