Anti-mech jump or motorized. Most Warrior House infantry is fluffed as being trained in anti-mech tactics. And you need the added mobility to close and execute anti-mech attacks.
Inferno SRM motorized or foot. The Cappies like to employ incendiary attacks, and these can be crippling in your timeframe when used en masse.
Mechanized scout/spotter. The Warrior Houses are fluffed as having excellent infantry scouts. In BT play, scouting is really about identifying hidden units, for which you want faster units to sweep out more of the mapboard faster, and that means mechanized infantry when assigning this role to infantry. They can also use their speed to keep a safe distance in the artillery/indirect LRM spotting role. Because these guys are about getting as many eyeballs in the field as possible, not firepower, I would deploy them as squads, not full platoons.
Towed Artillery/LRMs. As effective as field guns can be, they don’t seem to match the feel of the Warrior Houses. That said, the Cappies develop an appetite for artillery and minelaying, especially as the Arrow IV launncher and Thunder LRMs come into play. So I could see some towed Sniper/Thumper artillery and/or some LRM gun trailers in Warrior House infantry battalions.
Most of other roles they’re suppossed to be good at — infiltration, demolition, sabotage, assassination — don’t really translate to BT play except as part of the scenario setup. More AToW stuff.
A couple notional formations:
Anti-Mech Infantry Lance
Jump Platoon (Anti-Mech Trained)
Motorized Platoon (Inferno SRMs)
Jump Platoon (Anti-Mech Trained)
Motorized Platoon (Inferno SRMs)
Fire Support Infantry Lance
Mechanized Squad (Scout/Spotter)
Mechanized Squad (Scout/Spotter)
Mechanized Squad (Scout/Spotter)
Field Gun Platoon (Thumper/Sniper/LRM Gun Trailer)
Field Gun Platoon (Thumper/Sniper/LRM Gun Trailer)
Field Gun Platoon (Thumper/Sniper/LRM Gun Trailer)
The point being that the spotters and field artillery work together (obviously) as do the infernos and anti-mech attacks (the former cripples a mech while the latter finishes it off).
My head canon says two companies of the Anti-Mech Infantry Lances and one company of the Fire Support Infantry Lances per standard Warrior House infantry battalion.
Hope this helps.