Inner Sphere
Draconis Combine (Kurita)--Ancient Japanese-fixated culture. Bushido is a driving force in military matters. As such, House Kurita fields a large number of highly skilled MechWarriors whose approach to one-on-one combat comes closest to that of the Clans
Lyran Commonwealth (Steiner)--merchantile culture with a military burdened by 'social' generals (people given rank for political or monetary connections). Tend to make up military shortcomings by 'going bigger' resulting in such tropes as the 'scout lance' of Atlases. Currently the Commonwealth is part of the FedCom super-state, with a military largely organized on Federated Suns principals
Federated Suns (Davion)--field one of the largest, most competent armies in the Inner Sphere with a highly evolved combined-arms doctrine and military leadership that is skilled, experienced, and motivated.
Free Worlds League (Marik)--It calls itself a democracy and has a civil war at least once a generation. It's military is not as skilled as Kurita, as heavy as Steiner, or as developed as Davion. the FWL makes up for this by fielding the most technologically-advanced military outside of the Clans or ComStar
Capellan Confederation (Liao)--Laio forces are fanatical. Also adept at finding ways to use what they have, and sometimes field prototype tech in front-line combat. The Raven was a Liao attempt to revitalize electronic warfare, and they were the first to incorporate triple-strength myomer (which the Fed Suns
wanted them to do for...reasons).
ComStar--quasi-religious, officially-neutral, interfering busy-bodies. They have (they think) a monopoly on interstellar communications and are perfectly willing to use it to their own ends. Their goals fluctuate with who is in charge, but they've deliberately hastened the decline of technology in the past. Their military is equipped with Star League-surplus/vintage equipment which puts them up on the various houses, but they've only been organized a very short time, and while their training is generally good their actual combat experience is effectively nil.
The Clans
Smoke Jaguars--Highly skilled individually and hyper-aggressive. Poor management of civilian castes have seen this Clan thrive largely by seizing others' resources. They call it a 'Trial of Possession', but some spheroids regard it as armed theft writ large. Follow the Crusader ideology. Strongly believe in overwhelming force. Orbital bombardment is not out of the question.
Jade Falcon--Crusaders. The banking power-house of the Clans, their financial dealings have more than made up for other civilian-caste shortcomings. Their military is quite rigid in organization, communication, and doctrine. Generally will not discard zellbrigen (the Clan custom of single combat), or stoop to other dishonorable tactics. A few, however, are capable of being flexible enough to employ artillery, destroy civilian infrastructure if military necessity dictates, and the like.
Ghost Bear--Crusader today, Warden tomorrow. Steiner-like in a fondness for massive, hulking machines of doom and destruction. Notably does not employ aerospace-genotype instead using MechWarrior for pilots. Competent, noble, and not without a sense of humor (they once wagered a planet's future loyalty on the outcome of a game of North American-rules football).
Clan Wolf--even split of Crusaders and Wardens with Warden-leaning leadership. Long-range planners, with an even-handed approach to integrating new territories has ensured they take more planets faster, while their newly occupied territories are not as rife with rebellion as other Clans. Tactically flexible, notably they came up with the headhunting tactic, and they include specialized artillery mechs in front-line galaxies despite the Clans general view that artillery is not honorable.
Steel Viper--a reserve Clan, Crusaders. Probably the best strategists in the Clans come from Steel Viper, but were not active in the Inner Sphere long enough to develop appropriate tactical response against typical IS tactics. Still, senior leadership at Tukayyid recognized the disadvantageous position they were in early enough that when SV withdrew they suffered only 10% losses.
Nova Cat--reserve Clan, (generally) Warden. A bunch of dreamers. Their military is noted for any particular strengths, but neither does it suffer from any of the weaknesses some of the other Clans exhibit.
Diamond Shark--Reserve Clan, (generally) Crusader. Cut-throat merchants. Think Ferengi with Mechs. Don't make any deals with them because you'll lose even when you think you win. Their warriors are competent (the Clans don't have any warriors who
aren't competent), but new enough to the Inner Sphere that they don't really get that they aren't fighting bandits, or even other Clans.