A fireplace that is in constant use should have a larger indoor wood rack than one that is hardly used. This allows you to keep enough wood for the entire day without having to make several trips to the outdoor wood rack. The wood rack should not be so large that you are tempted to keep firewood in it for several days of use. Storing firewood indoors can lead to problems with insects in the home, according to the University of Wisconsin Extension. A small rack with just a few decorative pieces of wood kept around will not pose that much of a problem.
Wood racks must be sturdy enough that they don't tip over, light enough so that they can be carried to the outdoor rack without adding signification weight to the load and non-porous so that the inevitable dirt and debris do not fall out of the bottom onto your clean floors. If you are keeping it close to the fireplace, then it should also not be made of flammable materials.
An old wooden peach or apple crate gives a rustic look as a wood rack. It can be left natural or painted over to better fit your color scheme. A smaller steamer trunk has the advantage of keeping wood handy but out of sight when the lid is closed. An umbrella stand or a tall stock pot makes a good vertical rack for storing and keeping slender pieces of kindling away from larger pieces of firewood.
A whimsical note is achieved by using a child's large toy box as a wood rack although you might want to only do this in a child-free home to keep curious young hands away from danger. An old, wicker-style laundry basket with handles is light-weight, strong and easily painted. Line the bottom with plastic to prevent dirt from seeping through and you have both a basket for carrying wood and a wood rack for keeping it by the fire.