I completely agree with Steve81, TLS Guy, and KenM above, about both questions, cabinet wood and speaker cone materials.
A speaker cabinet should be made as inert and resonance free as possible. That's why MDF is used so often. It is much more resonance free than any hard wood. Good quality, void-free plywood can also be used.
In addition to the inherent resonance of any hard wood, as well as the expense of exotic woods like bubinga, there is also the problem of dimensional stability. Solid wood expands and shrinks as the humidity changes through the seasons. This will happen even if it is kiln dried and elaborately sealed on all sides. A six-sided box, a speaker cabinet, made from solid wood will become so stressed by these dimension changes, that the wood can split. It may take 2 years to happen, but it will happen. MDF doesn't expand and shrink as the weather changes. It's surface remains flat allowing for easier finishing. There are stunning looking bubinga veneers I've seen. I don't know their cost, but if you were considering solid bubinga, you probably weren't worried about that.
Now to your question about cone materials. Much is said about the sound qualities of different cone materials, especially woofers or mid wooofers. Some people swear that the sound from one type or another is the best. Others say a properly designed crossover can make any driver sound good without revealing the material of the cone. The reason is in the higher frequency behavior and misbehavior of the woofer, and how that varies with the cone material. Here is some reading on the subject:
First read Crossovers 101,
http://www.salksound.com/wp/?p=135. It's short and informative. It walks you through a simplified version of designing a crossover for a 2-way speaker. You should read the whole article, but I'll focus only on what its says about woofer cones at high frequencies. It shows the raw frequency response curve of a 6½" metal coned woofer, that could be aluminum or magnesium alloy.
The writer, Dennis Murphy, says, "As for the mess from about 4,000 -8,000 Hz–a lot of that is due to natural resonances at higher frequencies that are inherent in the cone material and the whole mechanical system formed by the cone, surround, and suspension.
That’s the dirty little secret of most woofers, and, as we will see, a large reason why good crossover design is so important."
Similar misbehavior (sometimes called "break-up") happens at higher frequencies for any woofer regardless of it's material. It varies with the size of the driver and the material of the cone. Larger drivers display their misbehavior at lower frequencies than smaller drivers. Also softer more flexible materials, like paper or plastic, display that misbehavior at lower frequencies than stiffer materials, like glass or carbon fiber, Kevlar, or metals. But the stiffer materials usually behave much worse that softer materials. Murphy's major point about this problem is that the crossover must filter out those resonances so the listener doesn't hear it. Some other speaker makers choose the exact opposite. They deliberately want to show off their cone material as a marketing feature. B&W is notorious for wanting everyone to know their speakers feature highly resonant, and sometimes harsh sounding, bright yellow Kevlar cones.
Your next reading assignment is a "white paper" published by Harmon Kardon, written by Floyd E. Toole and Allan Devantier.
http://support.infinitysystems.com/home/technology/whitepapers/cmmd.pdf
It discusses in more detail what happens as speaker cones go from soft flexible materials like paper or plastic, to stiffer materials. While this is a good treatment of the subject, remember that it also intends to market the ceramic metal matrix cones sold on Infinity speakers. ("Ceramic Metal Matrix Diaphragm" is HK's marketing term for a type of aluminum oxide commonly known as alumina.) It's major point agrees with Dennis Murphy, in that a good sounding woofer or mid woofer should be filtered by the crossover to suppress the misbehavior noise in the upper frequencies. Their point about their own CMMD product is that, compared to bare aluminum cones, their aluminum oxide coating raises the frequency at which the misbehavior noise begins. It makes the job easier for the crossover designer. Similar results are found in magnesium oxide cones in the Seas Excel drivers, and a hard brittle white ceramic material in Accuton woofers. Both of these makers produce expensive but very good sounding drivers.
Hope this answers your questions.