What have you found in your price range?
Does your budget include mics and video lights (for the interview)?
Low light and good video capture behavior = large lens diameter and large imaging chip (to let light in and to process the available light).
Thank you for letting us know the editing software. Can you provide any information on the computer hardware to be used for editing? Does it have a firewire or IEEE1394 port? How much RAM and available hard disc drive space? Are you willing to invest in an external hard disc drive? What are your plans for the video a year, 3, 5 or 10 from now - or is it just discarded after editing and posting?
The video to which you provided the example link was standard definition video in 4:3 aspect ratio. Is that what you want?
Space looks challenging. Keeping steady looks like a priority.