The intro box set 'mechs can be used with any.
If you want to more sterotypical.. the following tend to be more faction specific.
Kurita: Panther, Jenner, Dragon
Liao: Vindicator
Davion: Enforcer
Marik: Hermes II, Cicada
Steiner: Zeus, Commando
As for rulebook, I imagine the majority either use the 2nd printing, ignore the errata, or copy only those pages they care about. Also, a large part of the errata to the 1st printing is from the Companion. Several sections of it were declared standard rules, so they were included in the 2nd printing and thus became errata to the 1st printing.