Take note that if your GM is disallowing regional traits, it's possibly due to the campaign not being set in Golarion; if so, religion traits are also going to be hindered if there are no deities in common.
For Alchemist-friendly faith traits, I like Principled. It's very easy to match the fluff of and gives you a bonus against the saves that matter most. The loss in Bluff is probably meaningless if you're tanking Charisma anyways.
Firebug, as you've mentioned.
And any flavor of +1 Will.
if you want increases to initiative you could just take reactionary. Seems simpler than all that adoptive stuff, I don't think they stack as they're both trait bonuses so its probably not worth taking both.
I'm a really big fan of Clever Wordplay (Social) if you've tanked your Charisma.
I think I'd lean more towards Accelerated Drinker or Reactionary over Firebug - bombs just don't need a lot of help hitting, as it turns out. Accelerated Drinker doesn't help with extracts, but it's pretty easy to maximize potion value as an alchemist.
Indomitable Faith is probably the Faith trait that you want so that you can get a boost to your Will saves, and it's unlikely there are any other faith traits that will interest you.
Alternatively, if you feel like playing against type a bit, Purity of Faith (Religion-Iomedae) is an interesting option for a Religion trait, in which case you could swing over to Omen in Faith traits (which you could couple with Brushing Intellect in Social traits.)
