For Beginners
I suggest that when starting out you stick to the domestic hardwoods listed below. These woods are relatively inexpensive and are easy to turn. Eastern black walnut needs to be filled to take a gloss finish. Get claro walnut if available or use oil and wax on eastern black walnut to start with. Ash also looks good with an oil and wax finish. You can do just about anything to North American cherry and it will look good.
Cherry
Ash
Walnut
Mahogany is not a domestic wood, but it is easy to turn and takes a nice finish. And it is only a bit more expensive that those listed above. Honduras mahogany is what you want -- definitely not Philippine mahogany -- which tends to be too soft and is often stringy.
To try something harder than those woods mentioned above, try North American hard maple or osage orange. These two woods are also reasonably priced and turn and finish very well.
The following North American burls make good boxes but they are more expensive than the woods mentioned above:
Box elder burl
This wood is a cream color and is very soft but turns well and finishes well.
Big leaf maple burl
This wood is a tan to dark brown in color. Turns and finishes very well.
Myrtle burl
This wood is also variable in color. It varies from a light tan to dark brown. It is harder than maple burl but turns and finishes well. It is prone to checking so make sure it is dry or, if not, rough turn and let dry prior to completing the box.
Redwood burl
This wood is very attractive; lace burl is especially nice. Redwood lace burl is double the price of common redwood burl. It is somewhat soft but turns and finishes well. The dust from redwood is very irritating -- take precautions.
Those With Some Experience
Once you have acquired some experience turning boxes, you will probably want to try the exotics. Exotics vary wildly in hardness and turning difficulty. For an initial trial I suggest the following:
African padouk (pterocarpus soyauxii)
This wood is medium in hardness and turns and finishes very well. It is still one of my favorites. The dust will stain clothes and skin a red color. Moderately priced.
African shedua (guibourtia ehie) aka amazaque, amazakoue or hyedua
This wood is relatively soft and looks a lot like American walnut. It turns easily and finishes well. Moderately priced.
Australian she oak (allocasuarina fraserana)
This wood is a warm brown to red in color. It turns easily and finishes well. Being from Australia and Tasmania, it is more expensive that domestics.
English brown oak (quercus robur)
This wood is a warm brown -- darker than North American oaks -- and is very easy to turn. It finishes well. I prefer an oil finish on this wood.
Goncalo alves (astronium fraxinifolium)
This wood is hard but turns and finishes very well. It continues to be a favorite of mine. Moderately priced.
Imbuia aka imbuya (phoebe porosa)
This wood has a spicy smell that fills the workshop when turned. It is moderately hard and turns and finishes well. I use it frequently. It is a medium brown in color. Moderately priced.
Pear (pyrus communis)
This wood is pinkish in color when steamed and is moderately hard. It turns and finishes well. Moderately priced.
Putumuju aka canary wood (centrolobium spp.)
This wood is a lovely orange color. It is moderately hard. It turns and finishes well. Moderately priced.
With even more experience, you will surely want to try these.
Rosewoods
Any of the rosewoods will turn well and take a very good finish. They are hard; some are quite hard. Try them when you are somewhat experienced and your confidence in your skills is at a high level. I frequently only wax rosewoods, believing that they need no finish at all. My favorites are:
Honduras rosewood (dalbergia stevensoni)
This wood is a reddish brown color. Turns and finishes very well. Has a pleasant smell. The sapwood is a light cream color and makes a nice contrast with the dark heartwood. Moderately priced for exotics.
Tulipwood (dalbergia frutescens)
This wood is a pale straw color with red streaks. It is very attractive and the color is quite variable. It is moderately hard. It is more expensive than many of the rosewoods.
Cocobolo (dalbergia retusa)
This wood is red with dark brown or black streaks. Very attractive. Turns and finishes very well. It is very oily and quickly clogs abrasive papers. It is very hard. Moderately priced for exotics.
Kingwood (dalbergia cearensis)
This wood in a dark pink in color with black streaks. It is very attractive. Turns and finishes very well. It is increasingly difficult to find and is somewhat expensive.
Parakingwood (dalbergia pacifica)
This wood is a purple color with black streaks. It looks a lot like cocobolo, only with a purple color. It turns and finishes well. Moderately priced for exotics.
Violet rosewood (dalbergia louvelli)
This wood is a deep purple color. It may have black streaks. It is quite hard but turns and finishes well. Moderately priced for exotics.
Rio rosewood ( dalbergia nigra) -- very expensive now.
This wood is almost black with streaks of purple or very dark red. Some pieces are a very dark brown. It is under an import ban similar to that placed on ivory. Any that is available will be from managed forests and will be expensive. But it turns and finishes very well and has a very nice smell. It is well worth looking out for.
African blackwood (dalbergia melanoxylon)
This wood is jet black. The sapwood is a cream color and the contrast can be striking in a turned piece. It is very very hard and is sometimes difficult. But it cuts cleanly and finishes beautifully. Definitely not a wood for beginners.
Madagascar rosewood ( dalbergia baronii ) aka voamboana, hazovola, sovoka, sovodrano, hitsika, tsiandalana, palissandre
This wood, like all rosewoods, is very hard. It turns well and takes a nice finish or polish. Not all that common but worth looking out for.
Once you have tried all of these, there are dozens if not hundreds of others to try. Enjoy!