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Miro sorry it took a bit for me to get back to you....
As you can see our hard working forum administrator has merged this thread with the main one on the topic. And because of it there is probably a lot more information here now than you will be able to read in even a couple of sittings.
But to answer the specific questions you asked me, and since I don't know how much you already know or not I will go into detail. I'm sorry if I am wasting your time telling you things you already know.
I decided to use quartersawn mahogany because it is much more stable than flat sawn mahogany. Most people know that wood shrinks and expands as it takes on and gives off moisture. What many people do not know is that the amount of movement varies based on the orientation to the growth rings. For example, for all practical purposes wood will not shrink or expand in its length. While not 100% true the amount of change is so small it usually is not worth considering.
Take a look at the drawing below. If you were looking at the end of a log that was being cut into lumber you can see the boards I have labeled as flat sawn have a different orientation to the growth rings than the boards I have labeled as quartersawn. The growth rings are for the most part perpendicular to the face of the board in the quartersawn boards and they run more parallel to the face of the board in the flat sawn. Flat sawn boards will shrink and expand almost twice what a quartersawn board will. In addition because of the orientation of the growth rings they will tend to cup and warp much more than quartersawn boards.
To illustrate my point you could expect an 8" wide flat sawn board to expand by .05" when it goes from 8% moisture content (a good level for furniture building) to 28% (saturation point) while a quartersawn board would only expand by .03".
As far as where to buy the material that depends on where you live. Some parts of the country have much better access to lumber than others. I would look first in the yellow pages for hardwood lumber retailers. Then call cabinet shops in the area if you cannot locate anyone you can buy from direct. They will often sell you what you need with a small markup for their trouble. And if all else fails do like I did and search on the web.