We've tested numerous batteries and we highly recommend using rechargeable batteries over disposable batteries.
Through testing, we've found that Tenavolts will provide the longest and most consistent playing time with the ToneWoodAmp.
Tenavolts will provide 150% of the playing time that alkaline batteries will provide. In addition, there is no gradual power degradation or sensitivity to peaks that other batteries are prone to. As other AA batteries drain power, they fall below 1.5 volts. Tenavolts will provide a constant 1.5 volts.
Tenavolts charge in less than 2 hours and are good for 1,000 charge cycles, thus reducing battery waste and the cost associated with using alkaline batteries.
You can order Tenavolts here: Tenavolts Rechargeable AA Batteries
As an alternative, we've had great luck with the Panasonic Eneloop Pro 2450mAh as well.