There are 7 Clans who participated in the Invasion of the Inner Sphere. There are a bunch of Clans who stayed in the homeworlds as well, but they wouldn't ever really have much of an opportunity to fight Inner Sphere opponents.
I'm not very familiar with what takes place after the Jihad period (which is like the 3070s), so I can't really help on that. But here's kind of a rundown of the original seven Clans. The first four (Jade Falcon, Wolf, Ghost Bear, Smoke Jaguar) attacked during the first year, and the next three (Steel Viper, Nova Cat, Diamond Shark) came in as "backup" later on.
Jade Falcon -- The honorable villain. They're jerks, but they generally keep their word. They are aggressive and mean, even for the Clans. They're always willing to fight, and are one of the strongest Clans around. While they are bad guys, they aren't really that much worse than some of the Successor States. Maybe the most interesting Clan, they hate the Wolves and are their chief rival.
Wolf -- The Mary Sue. They tried to prevent the Invasion in the first place, and when it became inevitable they realized the best way to save the Inner Sphere was to keep the bad guy Clans from reaching Earth first. They quietly worked against the others during the Invasion. The most powerful Clan, with some of the best mechs, the best warriors, the best leaders, the best everything. After the Invasion they have a split where the good guys leave and form their own Clan, and the Wolves left behind become villains, but I stopped paying attention at that point.
Ghost Bear -- The boring Clan. Slow and steady wins the race. They are defined by being cautious, and slow to change or take risks until they think everything through. They are a powerful Clan, and use big fast mechs and lots of Elementals. But they aren't really that exciting, and don't have as much info written about them as the other original four.
Smoke Jaguar -- The irredeemable villain. The Jaguars are everything bad about the Clans rolled into one. They are powerful, not because they are leaders in culture and science (like the Wolves), or economics (like the Falcons), but because they have big badass mechs and they are psychotically aggressive. They're the Nazis of the setting (and even have the same color scheme). Sometimes it's fun to play the bad guy though. Somebody the other day called them Clan Chaotic Stupid, and that's pretty accurate.
Then you've got the three "backup" Clans.
Steel Viper -- Assigned to the Jade Falcon invasion corridor to "assist" after the Falcons had a couple of setbacks, they are a-holes. They hate the Falcons with a passion, but they're jerks too. They are Smoke Jaguar-lite, just a lot less successful and with worse Battlemechs.
Nova Cat -- The religious Clan. They have visions, and smoke peyote and stuff. They switch sides in the 3060s and team up with the Inner Sphere. They are assigned to "assist" the Jaguars with their invasion corridor. Some pretty good mech designs that are specific to their Clan.
Diamond Sharks (aka Sea Foxes) -- Clan Ferengi. They are merchants, and they sell crap to everybody. They had an extremely limited role in the initial Invasion, only really appearing in the attack on Tukkayid (which, of course, they lost). They are more a plot device to let Inner Sphere players purchase Clan equipment than anything else.
Personally, I'd suggest painting up your Clan mechs in camo schemes instead of making them a specific Clan. There's no reason why Jade Falcon mechs have to be green, or Ghost Bear mechs light gray. Paint them something generic and you can have them represent any Clan you want.
