Why tile at all
Tracing produces the better looking guide. The shapes belong to the picture, the outlines follow real edges, and the printed page reads as a drawing rather than a diagram.
It also produces wildly uneven work. One region is the whole sky and another is a window frame, so the person painting it spends four minutes on one shape and two seconds on the next. Alone that is fine. Across thirty people painting the same picture it means half the room finishes and half does not.
A tiling makes every cell roughly the same size, which makes the work even, comparable and predictable. Each cell takes the average colour of the area it covers, so it never ends up the colour of one stray pixel. That is the whole trade: you give up the drawing and you get a worksheet.
Squares
The obvious choice and the right one for the youngest hands. A square is the shape a child already knows how to fill, the grid reads as familiar, and the edges are horizontal and vertical, which is easier to stay inside with an unsteady brush.
The cost is that squares emphasise horizontals and verticals in the picture whether or not they are there. A landscape tiled in squares acquires a faint architectural quality, which suits buildings and works against water.
Hexagons
The best general answer, and the one worth trying before anything else for anyone past about eight years old.
Hexagons tile edge to edge with no gaps, and because each one has six neighbours rather than four, an area of similar colour reads as a continuous field rather than a grid. The offset rows break up the horizontal banding that squares produce, so skies and water look far more convincing.
They are also more forgiving of a wandering brush, because the angles are obtuse. A brush that overshoots a hexagon corner does less visible damage than one that overshoots a right angle.
Triangles
A true edge sharing triangular tiling, which is unusual and worth having for the cases where it fits.
Triangles introduce diagonals, so they suit subjects that already have them: roofs, sails, mountains, anything with strong angular structure. They also produce the most graphic result of the three, which makes them the interesting choice for a display piece rather than a first activity.
They are the hardest to paint. The points are narrow, and at small sizes a triangle has less usable area than a hexagon of the same nominal size, so watch the readability warning more carefully here than anywhere else.
Triangles and hexagons combine cleanly with each other, because both are built on the same underlying grid. Squares do not combine with either.
Choosing quickly
Squares for the youngest, for anything architectural, and when the familiarity of the shape is doing useful work.
Hexagons for almost everything else, and always for skies, water, foliage and skin.
Triangles when the subject is angular, or when the finished thing is going on a wall and you want it to look designed.
And contour tracing rather than any tiling when one person is painting one picture and the drawing matters more than the evenness of the work.