I hope you're painting by now.
If not, I'd go to
www.camospecs.com and
www.unitcolorcompendium.com to look through schemes. The latter is unofficial but easier to browse. Some schemes in there are made up; they say so in the fine print. In those situations there isn't a canon scheme for that unit so you can do whatever you want. They usually link to Sarna (Battletech's unofficial wiki) and to Camo Specs, but their links to the latter are often broken so you'll just have to search for the unit name. It's worth verifying a scheme in Camo Specs before committing to it, though. Note that it's the text description that's canon, and you can interpret it however you want. Sometimes you'll see Camo Specs artists paint the same scheme fairly differently, like the darkness of the blue in Clan Diamond Shark's Beta Galaxy.
To narrow it down, since you've stated an interest in the Clan Invasion itself I'd stick to the Lyran Commonwealth (which was part of the Federated Commonwealth ("FedCom") at the time), the Draconis Combine, the small Free Rasalhague Republic between them, and the invading clans: Wolf, Jade Falcon, Ghost Bear, Smoke Jaguar. The Nova Cats, Steel Vipers, and Diamond Sharks reinforced them and participated to varying degrees. Certain clans focused on certain Inner Sphere nations but I don't know the invasion corridors well enough to say which matches with which. If you want more choices among Inner Sphere nations, Federated Suns units were also sent to resist the invasion as part of the FedCom, and a whole bunch of nations, including from the Periphery, sent units to help smash Clan Smoke Jaguar in Operation Bull Dog and with Task Force Serpent towards the end of the Clan Invasion era (3058-'61). Look those up in Sarna, pick a unit, look up its colors, repeat ad infinitum.
Have fun!