Fine boxes are generally made from wood milled from hardwood trees. These are mainly broad-leaf and deciduous in temperate and boreal forests (losing their leaves annually) and evergreen in tropical forests.
Hardwood timbers differ from softwood timbers mainly in their method of reproduction and not necessarily their hardness. A hardwood like Balsa wood is much softer than many softwoods and would be of little use for fine boxes. Conversely, a softwood such as Yew is very hard and is popular for both fine boxes and fine furniture.
Hardwoods often have more intense colours than softwoods and are used decoratively as solid timber, veneer and inlays.
Below is a list of typical hardwoods that I can work with to produce a beautiful decorative box for you. Spend some time looking at the colours and grains to get an idea of the hardwoods that may interest you. Please note that the colours and grain patterns are representative of the wood, as this is an organic material there will be differences in the selected woods.
Many of these species have quite interesting variations that may be workable in solid form such as Pippy Oak, fiddlebacks, and certain burrs with wild grains. But the very nature of some of these variations means that some woods are only workable in veneer. See veneer for fine boxes for an explanation of veneers, parquetry, marquetry and inlays.