Try the Sony HDR-CX405. It is a great low light camera so you can film early and late. You can buy them reconditioned one for less then $200.

I had a Canon Vixia HF G10 that had a remote that would that would start the recording, zoom and take pictures.

I have given all of my video cameras to young kids to do outdoor videos for their youtube channels.

If you go online you can get most cameras refurb a lot cheaper.