Choose wood of uniform and even grain. Avoid knots.
Easy working woods generally do not have great strength and durability.
All wood used for carving should be properly seasoned. Seasoning means the drying out of a proportion of the moisture in the wood. It takes many years to season naturally but modern methods reduce seasoning process to weeks. Artificially seasoned wood is quite satisfactory. Unseasoned wood will crack and warp.
To season wood Eric Bramall's method was to cut it into suitable lengths, put under the workbench, and leave for several years. It needs to be in a dry place, and preferably warm.
Even seasoned wood can crack due to changes of temperature. With heads if you hollow them out it not only reduces weight but also reduces strain and minimizes the risk of cracking or warping.
If a crack develops whilst carving fill it with beeswax. This protects the edges from splintering whilst cutting.
Oak: One of the best woods for carving. Carves easily if tools are very sharp, holds detail, and is very strong. Good for marionette feet and hands which need weight, but heavy for heads. These would need to be hollowed out. Sharp chisels are essential, plus the ability to keep them sharp as they blunt quite quickly.
Walnut: several kinds, but most are even grained and suitable for carving.
Satin walnut: not a true walnut. Easy to work and useful for early exercises.
Pine: a soft wood. Suitable for practice but dull tools will crush and tear it.
Mahogany: many kinds - most are suitable for carving, qualities similar to walnut.
Sycamore, lime, pear: all close grained and good for puppet work as they can hold delicate detail. Most fruit woods good.
Birch: medium hard but pleasant to work. Not very durable.
Teak: not unlike oak - blunts tools easily.
Ebony and lignum vitae: Extremely hard and though they can be carved they are best avoided. Also lignum vitae is very heavy - the heaviest known wood.