There are three essential things to keep in mind when buying wood for Intarsia: grain/figure, machine ability and color/species—all of these are interrelated. It may be that you are looking for an exotic redwood only to realize too late that your saw won't cut it and when planning an intarsia pattern, the two most crucial points are wood color and grain relationship. That is you will need to balance the technical problems of dealing with different species against the artistic flow of the wood.
Grain / Figure
Use grainy as opposed to figured woods since the latter tend to be a money pit. For the parts of your project where you want to depict direction or action, go with grainy woods like ash and oak and for any metallic surfaces, opt out for non-grainy wood like maple or basswood.
The only exception for opting for a figured wood is when you're looking to feature interesting knots or other defects, as it were in a unique position in your pattern.
When choosing Intarsia woods, one of the most important things to keep in mind (particularly if you are a beginner) is their ease of use. While exotic woods have great color and figure they can be incredibly frustrating to sand and cut; they tend to cut better on heavy duty machines and might burn on light weight machines.
With light colored woods you need to be wary on what you pick and since the tendency of most beginners seems to be to go for the construction species because of their cheap price and easy availability, they overlook the tendency of the species to splinter, emit sap and difficulties in trying. Instead, we would suggest opting for pine, basswood and/or poplar. All of these are easily machine applicable and have the reduced tendency to splinter.
With dark woods the top choice in terms of both ease of cutting and cost would be cedar although with its strong fibrous grain, it does not make the best choice for cross-grain cutting. While both walnut and cherry are great substitutes in terms of their grain quality, they are also significantly more expensive. When working on a small project use wood thinner than 1" which is easier to cut.
Color / Species
An important thing to keep in mind when choosing an exacting stock of wood for Intarsia is differences in color between heartwood (reddish brown or gray black) and sap (very white). Some woods tend to darken the more they age with cherry being the best example. It starts out with a light tone and then ages to medium or dark shade when exposed to sunlight. Other woods like cedar have varying tones within one board which can inadvertently show the depth in your project. We would suggest keeping a set of these to choose from.
When it comes to the wood finishes they tend to darken the wood's original color and it itself ages with time. So the solution here would be to anticipate this behavior and allow room for it in your conceptual design.
But as with anything, you will get better at wood selection over time and with consistent practice. Never be afraid to experiment with what work and what doesn't and before you know it, you will find you have a knack for choosing the right wood for the right Intarsia project.