AC adaptor
Power cord

These are needed to connect power to the dock ("HandyCam station"). Allows recharging the battery (when it is in the camcorder) without having to get an external charger. I'd say they are required.

Handycam station
Since the DCR-HC96 has few "built-in" interfaces, the dock is required.

Wireless remote commander
Optional - but depends on your needs. You can control playback and recording from the camcorder.

A/V connecting cable
Optional - but depends on your needs. If you use the camcorder as the playback device, then required. As well, if your computer has not firewire port and you want to get the video into a computer for editing, then this AV cable will allow connection to an "analog/digital converter".

USB cable
Optional - but depends on your needs. You can probably find cheaper non-Sony-branded ones. If you use the camcorder to take stills that are recorded to the memory stick, then this cable will allow transfer of the stills - I would suggest/prefer using a card reader. The last one I bought at Fry's Electronics was $5.99.

Lens cap
Optional - but depends on your needs. Protects the lens when the camcorder is not in use.

Rechargeable battery pack
Allows using the camcorder without an external power connection. I's say this is important to have - but if you have no intention of recording new video then unnecessary. If you are planning to start recording and using the camcorder then a high capacity battery is preferred. They cost more, but will last a lot longer than the short-life battery that came in the box with the camcorder. I would get a Sony-branded one. See page 16 in the manual.

CD-ROM ?Picture Package Ver. 1.5.1?
Useless. Unneeded.

Operating manual (downloadable)
Free: http://www.docs.sony.com/release/DCRHC36-46-96.pdf

If you want to edit the video or otherwise get the video into your computer:

The Sony DCR-HC96 is a miniDV tape based camcorder. You already know this.

To get to the video in the camcorder (miniDV tape) to a computer, you need a Firewire cable (not USB) to connect the DV port (not USB) on the camcorder to the firewire port (not USB) on your computer. You did not tell us which computer hardware you are using. Firewire, IEEE1394, DV and i.LINK are all the same thing.

USB will not allow importing high quality, DV format video. USB-to-firewire cable/converter/adapter things will not work. In this case - the USB connection will get you to the memory stick used only for stills (apologies for being redundant). If your computer has no firewire port, hopefully it has an available expansion slot so you can add one.