I think that is going to be a cool drum!
It is hard to tell in the pictures for sure, but it looks like a material that was around a few years (maybe 10 now?) ago that is essentially a "manufactured" bird's eye maple.
It is an interesting and complex process, but they 'insert' the figure (looks like bird's eye) into a block by rolling veneer and drilling angled holes in a block of material. Once it is all set up, they shave off veneer in the normal manner, and it looks sort of like your pictures. I could be totally wrong too, but that's what it appears to be to me. I think Joe Montineri had some in his shop which was the first time I saw it 'raw'. I don't know if he ever used it or not (or maybe I saw it somewhere else too??)
That stuff you have is very interesting if it is what I think it is, because if you stain it, it takes the stain at extreme variances due to the mix of grain direction- even more so than flame or bird's eye maple (which can be very tricky). On the other hand, because of this, make sure you TEST on some scrap if you intend to stain it directly, because it could end up A LOT darker than you intend it to be. It is safer to stain the clear:
When ever I wanted to "stain" figured wood, I always lay down a coat of clear, and then a coat of tinted clear, so the color is uniform. I have also done stain the wood, clear, tint the clear for sick depth, but that is VERY tricky to get right (and a huge mess to clean up if you don't!)...
This is how I did it 99% of the time:
1) sanding sealer. Always.
2) sand smooth (make sure all wood is covered) maybe 320 grit dry. If you blow through, add a couple coats and re-sand flat (always with a block!) de-dust after sanding.
3) clear (a single wet double coat should be fine if the sealer was done well, and sanded smooth)
4) tinted clear (to 'taste'- sunburst finishes are easy this way too, because if you screw up, you just sand off the color- nothing is soaked into the wood)
5) final clear- probably three wet double costs will be plenty, if your base is flat.
6) block sand to 1000 grit in steps from 400-600-800-1000 wet with a single drop of dish soap
7) buff
8) wait... until you no longer smell the solvents from your finish
9) wax once it stops 'stinking'
10) assemble. I suggest wearing white cotton inspection gloves to prevent scratching the fresh finish. Try not to rush assembly until it stops stinking.
Tip: always apply as little finish as you can get away with.
When I did drums (for a local custom drum guy) I made a rack. It had a ~7" OD at the top and about 16" at the bottom- made from four pieces of 3/4" ply attached to a cheap 'lazy Susan'. I would tape off the ID, fresh tape the four 'legs', pop the drum on the rack and spin it by hand for a very even application of paint. He cut the bearing edges and snare beds before I did the finish, but drilled the holes after. Drilling before seems to make sense but the water from wet sanding can get to the end grain that way. You have to open up the holes after finish anyway, so you might as well wait... Sometimes the holes can be sealed with candle wax after painting but before wet sanding if you have no choice, such as a re-finish. When drilling through finish, you have to step up to diameter in small steps or you can shatter the finish. The other finish I used (acrylic eurethane) was more forgiving but would also chip if pushed too hard.
The gun I used back then was a very cheap 'detail' or 'door jam' spray gun you can get for about $20.00 at Harbor freight type places. I had about four of them- clear ALWAYS gets a dedicated gun. I used nitrocellulose lacquer for the drums (and vintage style guitars) and made my own tints from the Behlen line- mix a drop or two of color to a pint of clear... add reds and browns together to get the right dark brown for the edges of 58 replicas... And so it goes...
You can PM or e-mail me for more detail on anything if you want, but that's the basic program I used.Mind Blowi