The Greeks in the Aegean had access to a wide variety of indigenous and imported wood. Timber was imported from Macedonia, Thrace, Anatolia, and the Black Sea. We are lucky to have a textbook on trees by one of Aristotle’s students: Theophrastus on plants (Internet Archive) (ToposText)
ashen spears in Iliad, Tyrtaeus (Iliad 4.47, 19.390; Tyrtaeus 1.2.2, 19.10)
cornel-wood palta and (if we can trust Arrian who is alluding to the passage) xysta: Xen. Hell. 3.4.14, Xen. Horse 12.12, Arr. Anab. 1.15.5
fragment of pine in a sauroter in the National Museum, Athens: Kevin de Groote, “All your Strength is in your Spears,” p. 35 (academia.edu)
Pliny, Natural History 16.77 Bostock/Riley, 16.96 Mayhoff on which woods are good for making shields: vine (vitis), chastetree (vitex), willow (salix), linden (tilia), birch (betulla), elderberry (sabucus), and both kinds of poplar (populus). Remember that North American poplar is unrelated to Old World poplar! And European linden is the same genus as US basswood.
Theophrastus, On Plants 5.3.6 “The wood again of willow and vine is tough; wherefore men make their shields of these woods; for they close up again after a blow; but that of the willow is lighter, since it is of less compact texture; wherefore they use this for choice.” 5.7.6 “Willow is used for shields, hampers, baskets, and the like”
Pliny. Nat. 16.73 Bostock/Riley, 16.90 Mayhoff says that cornel (cornus) is used for hunting spears (venabula) and that elm (sambucus or sabucus) is best. It is good to know that cornel cherry is a type of flowering bush with bright red berries, and is not related to the cherry tree with hard stones in its fruit. Cornel is in the same family as dogwood.
Pliny Nat. Hist. 16.83 Bostock and Riley = Plin. Nat. 16.103 Mayhoff says that ash (fraxinus) is the most flexible wood for working, and that it is even better than hazel (corylus) for spears (hastis), lighter than cornel cherry (cornus) and softer than sorb-apple (sorbus)
The vast Persian empire contained a wide range of useful trees, and the Persian peace encouraged trade and long-distance travel. The excavations at Hasanlu revealed objects of white poplar (not the New World tree often sold as poplar today!), ash, elm, boxwood, maple, juniper, prunus (almond or peach), and other woods. The bronze mace with a boxwood handle and the possible spear socket on an elmwood shaft might be of interest to people reenacting soldiers. In the salt mine at Chehrabad, they found pick handles of Eurasian poplar (poplus sp.), European ash (fraxinus excelsior), Manna ash (fraxinus ornus), maple (acer sp.), and cornel (cornus sp.), some tamarisk used in other functions, and some stone fruit (prunus sp.) and apple (malus sp.) used in other functions. The arrows from Persepolis were mostly mounted on reed shafts via wooden foreshafts (Schmitt, Persepolis II p. 99, Hulit’s PhD thesis has diagrams of how such arrows are assembled). If a wood is appropriate to the task and native to Eurasia, it was probably used for that task somewhere in the Persian empire.
Mary Virginia Harris, “Glimpses of an Iron Age Landscape: Plants at Hasanlu,” Expedition Magazine Vol. 31 Issues 2, 3 (1989) pp. 15-18 http://www.penn.museum/sites/expedition/?p=2473
… persepolis II …
Nicole Boenke, “The Achaeobotanical Record,” Metalla: Forschungsberichte des Deutschen Bergbau-Museums 21.1–2/2014, 2015, pp. 60-74
Ancient woodworking based on wedges, adzes, and chisels followed a very different logic than modern woodworking which starts from homogeneous boards cut with saws and planed smooth. Books on ancient shipbuilding, architecture, and furniture will get you started. On the other hand, lathes were used for working wood and bone (chariot axles and spokes, throne legs at Persepolis, a knife handle at Chehrābād), and those crafts may have been more similar to their modern counterparts.
Caroline Earwood, Domestic Wooden Artefacts: in Britain and Ireland from Neolithic to Viking Times (Liverpool University Press, 1993)
Peter Ian Kuniholm, “Wood” in Eric M. Meyers, ed., The Oxford Encyclopedia of Archaeology in the Near East, New York, Oxford University Press, 1997, pp. 347-349 https://dendro.cornell.edu/articles/kuniholm1997b.pdf
Postgate, J. N., and Powell, Marvin A., eds. Trees and Timber in Mesopotamia. Bulletin on Sumerican Agriculture, Vol. VI. Cambridge, 1992
Meiggs, Russell (1982) Trees and Timber in the Ancient Mediterranean World. Oxford, 1982.
Robert Ross (ed.), Wood handbook: Wood as an engineering material. General Technical Report, Forest Products Laboratory (USA), FPL-GTR-282 (2021) https://www.fs.usda.gov/treesearch/pubs/62200
Edit 2022-01-21: added reference to Xenophon’s cavalry commander and to Pliny
Edit 2022-02-12: added Kuniholm