No guitar amp is going to do the BeatBuddy complete justice, because they are just that - guitar amps.
PA with stereo setup is best. Next, consider using a powered monitor or main that is portable. Any 10", 12", or 15" powered main/monitor will be tailored for flat EQ response, and most now even have some basic EQ. For my acoustic gigs I have a small setup with 2 10"/horn mains, and a powered 6 channel mixer. Plenty loud/clear for these gigs, and I can run BB in stereo.
And certainly the more clean headroom (power) you have in an amp the better. The goal is to reproduce the recorded wav sounds from the BB as accurately and uncolored as possible, since they are already “mastered,” unless one is intentionally trying to produce “Lo-Fi” sounds or such.