Bs and Ps all the way. Shouldn't really need As as much because it is already fairly good in that regard, Ts maybe (1s is okay). I'm never really blessed enough to have so many mods rolling all over the place that I can afford to be fussy, but if I did, Bs and Ps. I can always use more ammo and more damage. On everything.
As for your side question, this one is tough for me. If it came with the Nuclear Plasma Rifle above, I'd go for the Jackhammer. Why? Well, after emptying the Nuclear Plasma Rifle and waiting for it to reload, I'd be paranoid about getting caught with my pants down with the focused double shotty and needing to reload that too. With the Jackhammer, at least I'd have a lot more shots available to me before having to reload.
With Shottyman? Focused Double Shotgun.