Are you going to use the full 1000w? If so, you will be pulling 83+ amps (the inverters are not 100% efficient, only like 85%, so add another 15% to the 83).
. Where are you going to mount it? If it came with cables, it probably came with 2ga cable (2/0 would be way huge for that). 2ga is good for 181 amps, more than you need. It will take way more for short periods of time (duty cycle or in case of inverter usage, surge). 2/0 (or 00) would be way huge.
Your 1000w inverter probably surges to 1500w (to start motors and such),
I'd put it on a 150amp fuse. 99% of the time, your not going to be using that much of it (laptop =80w, coffe pot 400-600w, tv 200w). If your using motors, they like the juice, especially at startup.
I didn't put my 500w on a fuse. It's kinda of pointless to put a 120 150 amp fuse, if it shorts out at 80amps, it's going to spark anyway. The purpose of the fuse in this case would be to protect the inverter or battery incase of a short. If your mounting it close to a battery, I'd say definly no fuse required. It's your call though. Your starter cable isn't on a fuse, it draws about 80-100amps. If you did fuse it, go with a 150. If your not going to use the full 1000w, fuse it down at 80 or 100. Fusing it adds 4 high resistence terminations in the line (wire to terminal, terminal to fuse, fuse to terminal, terminal back to wire), causing a larger size wire to be required.
The reason the manual goes into all that detail is because people use battery banks (like a large boat, or an off-the-grid home), so they include text for various setups.
You are pushing the limits of your alternator and battery with a 1000w inverter, if you run it full titl for any period of time, you will drain the battery, even if the engine is running, unles you got a high-output alernator.
Here's a rough wire size chart for you to automotive usage. Note that
http://www.powerstream.com/Wire_Size.htm
Go with the chassis wiring column.