What paint should I use to paint a mural directly onto a wall?

You may compare features of 8 usual paints as below, then choose one upon your need and already mastered skills

1, oil paints

http://www.oilpaintingfactory.com/oil-painting-tec...

water soluble, not floating, rich colors, need high skills

2, acrylic paints

http://www.oilpaintingfactory.com/Acrylic-painting...

not water soluble, not floating, rich colors, need high skills

3, watercolor

http://www.oilpaintingfactory.com/watercolor-paint...

water soluble, floating, less colors, need high skills

4, gouache

http://www.oilpaintingfactory.com/gouache-painting...

water soluble, floating, less colors, need high skills

5, pastel

http://www.oilpaintingfactory.com/pastel-painting....

water soluble, not floating, less colors, easier

6, charcoal

http://www.oilpaintingfactory.com/charcoal-drawing...

water soluble, not floating, black and white colors, easier

7, pencil

http://www.oilpaintingfactory.com/pencil-sketch.ht...

water soluble, not floating, less colors, easier

8, wax crayon

http://www.oilpaintingfactory.com/wax-crayon-paint...

water soluble, not floating, less colors, easier

You have not given enough information.

Is the wall fresh plaster? Is it plasterboard? Is it plywood panels? Brick, Stucco, Inside or outside?

Is it a new wall or is it an old wall that has been previously painted?

If the wall is fresh plaster and located inside you may use tempera.

If the wall is previously painted in an oil base paint, you must use oil paints.

If the wall is previously painted with acrylic then you may use acrylic or oil based paints.Never paint acrylic on an oil base but you may paint oil or acrylic on an acrylic base.

Mollypitcher

No matter what the material of the wall, you can use Acrylic. Its a versatile paint and it dries quickly and its permanent on the wall. Use Acrylic. Tempera is water soluble and it wear with time.

Acylic.