I'd go for a bit heavier lineup, maybe it's the Coyote in me coming out.
ASF: Rapier. A great old SLDF standby, with a Royal version if they advance the tech along
BA: I'd go for the Infilitartor II (Magnetic). It may not have soe of the functionality of the Fa Shih, and has slightly less armor, but the Stealth, ECM, and MagShot are a great combo with many advantages over the Fa Shih in other areas.
Mech: If you're wanting engine commonality with the ASF, you have to take a 4/6 85 tonner. So I'd take the BattleMaster. It's got tons of variants to choose from, a gun for every situation, from MGs to a PPC, an SRM-6 with 2 tons of ammo for fun with different loads, etc etc. Even a couple of Royal variant if you progress that far. That said, I'd forget about engine commonality and go for a Black Knight, myself. I'm big on durable flashbulbs. No ammo, standard engine, several variants to choose from including a Royal, god speed, a good mech for commanders, battlefists for additional utility off the battlefield, and it's not an assault mech, which is probably a selling point as far as resource-intensiveness goes.