Wood makes a very stable surface for paintings, but can have problems with curling, splits or surface defects. There are ways to minimize this problem by how the wood is cut (either veneer sheets in plywood or solid planks,) and choosing species that have low shrinkage characteristics and take paint well.
Source: USDA Handbook Chapter 3, “Physical Properties and Moisture Relations of Wood”
How wood is cut:
Wood cuts are made lengthwise in one of two ways, tangentially or radially. Tangent cuts are sometimes referred to as “plainsawn” and radial cuts as “quartersawn” or “rift.” Tangent cuts are the most common at mills since there is less waste and is therefore less expensive, but this type of cut is more likely to lead to warping problems. As such, a radial cut is a better option for the surface of a wood panel. Potential drawbacks of a radial cut is that there is less surface area so they tend to be smaller in size, depending on the size of the tree, and for some species a radial cut may not accept paint as well as a tangent cut. Also, at most mills a radial cut option is not offered for many species.
How wood shrinks:
Wood is made mostly of tubular cellulose fibers that run through the inside of the trunk (picture drinking straws stacked side by side.) When wood absorbs or loses moisture those cell walls expand or contract and this action is what can cause the panels to curl or twist under the stress. Splits and cracks can form from the rays that emanate from the center. The greatest amount of stress occurs in a circular fashion, following the direction of the rings. Since a tangent cut has that stress at the sides, it’s more prone to warp. Radial cuts shrink at about half the strength of a tangent cut, and most of the stress is limited to the depth rather than the face, and is less noticeable. Splits or checks on radial cuts will not appear on the face.
In the image below the bottom panel is raw poplar, and sitting on top of it is a solid ¼” birch panel. Both are tangent cuts. The birch was painted with an acrylic primer and you can see how much it curled after drying. Even the poplar panel has a slight curl to it just from humidity, but the thickness helps lessen the distortion.
One interesting thing to keep in mind is that when trees grow at an angle instead of vertical, such as with large branches or split trunks, they tend to have more inherent internal stresses that can lead to later warping problems, regardless of how it’s cut. This trait is referred to as “reaction wood.” It’s not the sort of detail that is easily available, but it can cause a good type of wood to behave poorly.
This Wood Explorer site has a very thorough database that lists various wood species characteristics, including shrinkage and painting. Some hardwoods that take paint well and have low shrinkage are river birch, white ash, and yellow poplar. There can be differences in behavior within some species types (not all poplars are identical, for example) but they still tend to be rather close, usually depending on where they come from.
Composite panels made of high or medium density fibers (hardboard or MDF) have a more uniform smooth surface than solid wood, but they can still warp, and there’s no way to deal with it other than building a back bracing frame support. They can also have other issues, such as being made of low quality wood and a tempered surface that doesn’t paint well. Solid wood or plywood made of species with low shrinkage ratios, radially cut, tend to react very little to changes in humidity. Bracing is still a good idea, but a simple frame along the back edges (strainer) is usually all that’s necessary.
USDA Forest Service Documents
USDA List of Hardwoods