There is no easy answer (in my opinion) to beating each facility easily.
There are a few Guides on GameFAQ's which may help you, with pokemon teams and movesets for them and how to defeat a specific brain (facility owner).
The Battle Pyramid gives more BP on normal runs (meaning no Frontier Brain fight) than the other facilties, also, when you get two or three silver symbols (any of them) you can start betting on yourself with a person in the battle frontier (don't remember where).