Pretty much any mech could be a family mech. While heavies and assaults are bigger targets, they're also tougher, and lighter mechs won't cross them, even if they're heaviily damaged. Lights exist in greater numbers, while mediums are tougher and even more numerous.
What it ultimately comes down to though is: Is the mech in question still in production? Or at least still having parts made?
If so, then you're more likely to see them as heirlooms. Time and attrition would wear away at the numbers of OoP designs, reducing the likely hood of encountering one. Meanwhile, bug mechs are built in enough numbers to keep them in circulation, even if the pilots get stuck fighting things they shouldn't.
Most common however, would be either trooper mediums, who's numbers and tough armor keeps them going in the face of what they might run into, such as vindicators, enforcers, and centurions, or the four 55s (Griffin, Shadowhawk, Wolverine, and Dervish), which can outfight most things lighter, and outrun anything they can't fight easily.