I think a CoH style RTS would work best, being less about base building and just focused purely on combat.
The 3 doctrine system would also work well.
For NCR, the standard Infantry/Airborne/Armour would probably work for them. Armour in this case being centered more around PA units, though I'm willing to bet NCR could field actual working armoured vehicles without too much difficulty.
BoS is pretty easy, three doctrines are West Coast/East Coast/Midwest. West coast being an early game focused faction, East coast being a late game focused faction, with the Liberty Prime super unit of course and Midwest being good all around.
Legion would probably be Lanius tactics/Frumentarii infiltration/Native tribes. Native tribes being people like the Khans and White Legs.
You could probably toss in a special "Old World" faction, so you could fit in Enclave/Institute/House as a doctrine each.