Water-based finishes are still polyurethane or resins, but because it is made with water it penetrates deeper, dries faster and has a low odor. This type of stain is recommended for low-wear furniture. For children, this would be acceptable on a dresser or shelf, but not on a table, chair or bed, as those are touched often and wear down faster.
Oil-based finishes, such as boiled linseed, tung and Danish are more resistant to wear than water-based stains. Oil finishes can be reapplied, which is helpful if it gets scratched, but something like linseed oil needs to be reapplied, which can be time consuming. Keep this in mind when choosing an oil-based stain for children's furniture.
Varnish is a glossy finish that can be made with oil or with a synthetic resin. Varnish is durable, clean and resistant to most things, such as heat, chemicals and water. This is an acceptable finish for children's furniture, though it has an obvious and unnatural appearance. Shellac and polyurethane are both considered to be part of the varnish family.
Like varnish, shellac is a high-gloss finish that is applied with a brush or spray gun. It is durable, though it is susceptible to water and alcohol, especially if mixed with wax, which may dissolve the shellac's protection. On a play table or chair, this could be a problem, but is otherwise acceptable for furniture in a kid's room.
Polyurethane is very strong, but does not have much give. This can be beneficial for pieces of furniture that do not need to "move," but for something like a chair or bunk bed, it may not work well. It often looks unnatural or plastic. This finish can be used on certain children's furniture.
Lacquer is an ideal finish for children's furniture because it is durable, but also flexible. It is not difficult to apply to wood, and does not have to be reapplied. When applied, it dries quickly, with the chemicals evaporating. Jeff Jewitt, of Fine Woodworking magazine, states that certain types of lacquer can yellow over time.