I do a bit of woodturning (see
a few bits I've made) Exotic woods in flat form are quite hard to come by and expensive (see my post above). The reason I bought the laser was to cut veneer - anyhow I have tried quite a few woods and you will find the oilier the wood is the more smoke and less cutting ability due to the carbon build up.
Walnut did not cut well on my set up but this may be due to lack of a better air assist - teak was a bit better. The other problem you will find is the grain of some woods are tighter than others (depending on how fast the tree grows). This leads to inconsistencies in the material - spalted beech is a good example. Parts of the wood will cut well but where the grain is tight it does not cut as well - so finding the right setting can be trial and error and is different for each bit of timber.
Most wood will engrave ok - but again you can get some varying results for the same reasons above - pictures work well but the wood can be fragile on the darker areas so if rubbed too much will come off and leave light patches.
For signs - the easiest way would be to cut the shape on a band saw, route the edges and sand then engrave and finish with a varnish.
Most of my wood comes from a company called Timberline in Tonbridge or Stiles and Bates in Dover - both sell 'blanks' but I tend to buy 'planks' and cut to size for whatever job I have on. Depending on the size of the sign and the wood you will also encounter warping - as soon as you cut a plank down to a thinner size it releases the tension on the grain which causes the wood to warp. There are ways around this such as quarter sawing the blank into strips and then gluing back together!
Sorry to go on a bit but I hope it's useful
Dave