I am assuming they were originally a House unit, and their starter Mechs were from a House unit.
If so, how much of their salvaged Mechs belong to them, and how much to the House? This would be a way to make their merc force start a lot smaller, and with much less money than they were expecting. Plus, assuming they were ordered to defend a world, leaving would be essentially going AWOL, with House Mechs. They need to train up enough replacements to take their place, so the House doesn't lose any defenses.
If they found the gold and lostech, they will likely wind up trading most of that for Mechs that they can own. The other option is to go to Solaris VII, and buy damaged Mechs, with their techs to bring them up to better capability. Lots of politics here to make sure they get a good deal for the gold and lostech.
From there, since they are just starting out, their reputation will be rather low, so initial contracts will be bad options, low pay, or both. They will also need to hire a Dropship and Jumpship whenever they want to go anywhere.
Their best bet in the meantime would be improving their position at the House Court, so instead of taking assignments, they get to pick and choose their assignments. If they are in bad shape and need to repair, they take the Garrison/Cadre mission that a Baron needs help with. If they see a problem and want to shoot stuff, they join the existing forces of a Count's planet, and are first in line to deal with attackers (and their salvage).
Let them start out thinking that getting a Dropship is the key to making money. Let them have to deal with Dropship cargo fees, passenger tickets, etc whenever they have to rent a Dropship. That will encourage them to go after a Dropship and capture it. Once it is repaired, they use it to rapidly respond to attacks all over the planet. But when they want to go offworld, introduce them to the fun of Jumpship fees, scheduling, etc. The good part is they have FTL capability. The bad part is they need to keep the Jumpship fueled up, protect it from pirates (a carrier Dropship that is using up a Jumpship Docking Collar instead of making money), and shmooze their way to the top of the repair/maintenance queue at a shipyard when their systems need to be overhauled.