Guysonic is correct -- there's an internal jumper for selecting 6v or 12v operation. Internally, there's also a way to adjust the low-battery indicator and auto-shutoff threshold. At 6v, low-battery indicator is set for 5.75v and auto-shutoff for 5.0v; For 12v operation, low-battery indicator is set for 11.5v and auto-shutoff for 10.0v. Odds are if your box is marked 6v, it's calibrated for 6v, and you don't need to re-calibrate. If not, and you want to calibrate for 6v, there are directions for how to do so on the Grace website.
You may wish to identify whether your V3 falls into the range of units that has its digital output polarity swapped. This issue affects units with serial #s V3001-V3496. If your unit's affected and you want to get it fixed, I believe Grace will do it under warranty. Again, there's more info on the website.
As for power options, I used to use - and I believe plenty of TSers continue to use - rechargeable li-ion batteries marketed for DVD players. Just need to hack a V3 power connector onto the battery's cable. These batteries are 9v, but will work fine with your V3 if it's calibrated for 6v operation. (They will not work if your V3 is calibrated for 12v.) The V3's low-battery indicator and auto-shutoff features won't work because they're still calibrated for 6v operation, but these batteries have their own low-battery indicator lights, so it's not a big deal. Some TSers have referred to these li-ion batteries as "Wallmart" or "Wally World" batteries because at one point they were available inexpensively at Wallmart. Last I had one, quite some time ago, they were branded under several names: Initial RB-270, Lenmar DVD-U9, and Memorex something-or-other.