Mine likes most amps, except the few Deluxe types I've played. I have yet to dial in my sound through my TK Imperial. That amp loves everything else, but sounds only OK with the SC HB II. I actually put the HB away for six months or so after struggling with it and the Imperial for so long. I thought I might have been falling out of love with it. Nope. Still love it, just with other amps.
I run the piezo through a LR Baggs Para DI or Boss VE-8 if I'm singing, then straight to the PA. If I'm screwing around without the PA, I tend to NOT play the piezo.
As far as pedals, I run it through whatever the pedalboard has that day. I've been digging the Gamechange Audio Plus pedal a lot lately. I feed it the chord, then noodle, then move on through the progression. I haven't really found any pedals that don't work for my SC HB II.
Congrats on the HB! Tell us how you are running yours.