I'd go with a power supply... 9v 300+ mA, make sure polarity is right. Batteries never last long in pedals for me... usually 8 hrs max or no more than a few days (if u use a battery, unplug cables from the pedal between uses as they could be draining it). Everything on Noon should give you some of it's basic flavor and enough output. If you want the pedal to blast output, switch it to Line.
I actually sometimes run my BDDI into a Hartke 1x12 combo that one of the drummers I work with has. Works fine... got some great tones for the mix using that rig.
I have just recently started trying my Sansamp as a DI into a power amp. Not quite the tone I like but I am learning to use it better (I love the Sansamp but always hated it solo). For DI use like this I cut treble/bass a dash and use plenty of drive. To get a decent sound I really have to roll around the controls on my bass, mids on 10. I guess I use a *ton* of EQ and shaping on my heads to get my tones just where I like it.
The way I typically incorporate the BDDI is to run burly ass mids on my head and run the BDDI in the FX loop blended with a dash of its scoopy/presence/OD.