I've heard that you shouldn't house 2 triggers in the same tank as aggression can occur between them. That being said, a lot of people here on RC seem to do it.
As for fish to house with triggers, the fish should probably be at least similar in size to the trigger. Also, the trigger should be one of the last fish added to the tank as this will let the other fish stake out territory. if the trigger is added first it will be extremely aggressive to new tank mates-so I've been told.
Also, something to keep in mind with the picasso trigger (I don't know about the bursa) is that it is a slow growing fish. This should allow you some flexibility when choosing your initial stocklist as it gives the other fish a chance to outgrow the trigger. Finally, the picasso trigger will become more aggressive as it ages.
Hopefully this info helps-keep in mind I haven't kept a tank yet either but I've been doing a lot of research on livestock (especially the picasso trigger as it's the fish I most want

)
My planned stocklist for a 180g FOWLR is
Picasso trigger
Harlequin tusk
Blue tang or kole tang
one spot foxface
singapore angel
some species of eel
possibly another wrasse species
Maybe this will give you some kind of framework to plan your stocklist around.
Good luck, and hopefully you'll get some more experienced people chiming in shortly!