Camera recommendations for concert videography?

As the title states I’m seeking advice on a camera or camcorder which would be good for concert videography. The setting would be small concerts (meaning I’d never be very far from the performer) in which I’d be doing videography for friends’ bands, and of course low light would be the primary issue to deal with.

My goal with budgeting is a soft ceiling of $500, and a hard ceiling of $1000. The quality of the picture does not need to be HD, and I would be happy with older models which can be purchased used to stay within my price range.

My use of the device would be dynamic, so ease of focusing, maintaining focus during movement, and through zooms is a goal I have for the camera. A good zoom function is preferred as well.

My goal with battery life is at least 45 minutes so that I can be reasonably sure I can record a band’s entire set before needing to change batteries. More battery life is always better on that front.

It would be preferable to be able to easily transfer footage directly onto the computer, which I would assume means it would be a digital camera. If you know of a camera which satisfies all the other goals, but is not digital, please still recommend it, it’s not a deal breaker.

The camera would not need to have a good microphone built in, I plan on utilizing an external microphone to get the best audio quality, and be able to plug into a sound board.

Thank you, and please let me know if I let any parameters undefined. I tried to do research on my own but I’m still an amateur on the subject.