1. Homer, & Keep, R. P. (1897). The Illiad of Homer: Books I-VI. Boston and Chicago: Allyn and Bacon.
This is one of the many modern takes on Homer's Illiad; however, almost all versions can be utilized. The Mycenaean period is Homer's heroic age of the Trojan war, and his descriptions of weapons, armor, and fighting is decently accurate. Although, when Homer mentions any large number it is often good to take a zero off the end.
2. Snodgrass, A. M., & Snodgrass, A. M. (1999). Arms and armor of the Greeks. Baltimore, MD: Johns Hopkins University Press.
This is a well written and informative resource meant for a more general audience. It provides an introduction and discussion on Greek arms, armor, and warfare of all periods starting with the Mycenaean period, providing details without overly technical archaeological language.
The Mycenaean culture had a very militaristic nature, and is considered the period that Homer's Trojan war occurred. This militaristic nature is heavily represented in their art and writings. Military infrastructure, production, and logistics were all palatial controlled, with subservient towns and villages expected to provide men and supplies when called upon. Military endeavors would take place in the summer following the agricultural cycle, and occurring between planting and harvesting of crops when the seas were also favorable.
The Military composition of the Mycenaeans was built around heavy infantry with elites acting as cavalry or charioteers. Weapons used during this time included: spears, swords, bows, maces, axes, slings and javelins. For protections the Mycenaeans utilized tower or figure-eight sheilds while body armor would vary from heavry duty (the Dendra Panoply) to little or no armor; however, most elements of later hoplite panoplies are present. The most unique aspect of the Mycenaean arsenal was their boar tusk helmets.