I'm going to be using a lithium battery and a standard micro USB charger input. You can get complete lithium "battery management" boards that include the USB socket for peanuts these days. Some ones I bought for under $3 (including postage!) have the correct lithium charge cycle, over-current and over-discharge protection; even red and green LED indicators...
I've also got some surplus Samsung phone batteries (surplus because their owner dropped his Galaxy S4 in a puddle three days after I sourced them for him :-).
Some other postage-stamp-sized modules that can step up the 3.7V lithium voltage to as high as 50 Volts (adjustable) cost $1.39 if I remember correctly!
Yes, it's unfortunately extremely possible I won't much like the built-in effects. The Chinese seem to be past masters of producing what are potentially very useful effects, if used with discretion, but they never seem to think it's necessary to provide any way of adjusting the level!
Still, the EQ and built-in tuner could be probably be put to good use.