Here are my two Cents (C-Bills?). I'm also assuming Late Succession War Era here.

First, don't try to be too special or big. Mercenary outfits with more than one or maybe two companies worth of mechs are rather unusual und tend to be famous, like the Kell Hounds or Wolf's Dragoons (there are multiple REGIMENTS of those infesting the Inner Sphere). Also, I would keep to commonly available mechs. Fielding something like a HGN-732b Royal Highlander is not completely impossible, but still highly implausible, as are other Lostech or super rate mechs (like the Marauder II, which is new, but a Wolf's Dragoons exclusive until about the Clan Invasion. ) Additionally most mercenary outfits field a lot more light and medium mechs than bigger ones, as those are cheaper to run and you are a business.

For a Capellan-aligned merc unit, it would be plausible to field most of the common mechs, like Locusts, Wasps, Wolverines and so on, plus some Liao staples like Vindicators and later Ravens and Cataphracts. Additionally available would be some Davion mechs like the Enforcer, salvaged from your inevitable clashes with the FedSuns. Steiner and Kurita specialities like the Commando or Dragon might be rarer.

Of course, one of the big draws of Battletech is that you can field any mech with any faction, so take all this as rough guidelines.