Hi8 is analog. That means:
1) connecting the camcorder's AV cable to the camcorder and an "analog/digital converter". This can be a "capture card" or low end external USB unit (check Roxio, Pinnacle Dazzle, Hauppage among many others) or the good external ones use firewire (Canopus ADVC55) assuming your computer has a firewire port.

2) connecting the camcorder's AV cable to a "direct to DVD burner". There are several...

As for the new camcorder requirements...
The closest/best - in my opinion - is probably in the Canon HF S series, but you will be hard pressed to find that zoom. All video files are "Easy transfer to pc hard drive" whether the camcorder is digital tape, flash memory or hard drive - assuming the computer is appropriately equipped. Since we don't know what computer you are using, we don't know if the computer hardware, operating system or video editor will be able to deal with the high definition files.

Batteries in the box generally do not last as long as you need; optional high capacity batteries are available from the manufacturer.

Good low light behavior = large lenses and large imaging chips. These will add to the expense of the camcorder and likely push you out of the sub-$500 area.