I'd be most interested in splitting the difference, ie a House merc. A unit like the Kell Hounds, Eridani Light Horse or the Northwind Highlanders, they have a long term garrission contract with a house but they then have supplemental contracts sending smaller forces out on individual contracts.
Personally I have a few ideas:
1)All the players are independent of each other and on either Galtea the Merc world, or Solaris, and one of the players, or an NPC is putting together a merc unit, hiring people with Battlemechs or infantry training, or tech training, or whatever.
2)A conventional lance, or some other force in one of the house militaries
3)An unconventional house force, like what Katrina Steiner did with the Red Corsairs, or Death Commandos, or any intelligence service
4)Or we could just play some pirates
I like number 1 the best, it gives us the chance to interact getting to know each other, it also gives us a big hand in forming it. I like that it also removes the ability to have seeming unlimited resources as a house unit.
If we go with Merc I have an Idea or 2, The first is a distant relative of the Steiner Family who left in disgrace after her Company (Isn't nepotism grand?) was ambushed and destroyed by a Kurita ambush, she was ransomed off, and offered another command but it was only a ceremonial one with absolutely no chance of combat, so feeling bitter about it, she leaves, heading to a Merc recruiting world under an assumed name to hide any difficulties brought about by her past. She would be a good but not very experienced mech warrior who is dispossesed.
Is there any bonus for being dispossesed since the size of your battle-mech seems to be factored into your other stats. I would want Her to start dispossesed but later pick up a mech at some point during the game as salvage, or buy stealing one in furtherance of a contract.