1 - Inverters are grossly inefficient. A DC-DC power supply is a better way to go. However, based on your system specs, there is no DC-DC PSU that would meet your needs.
2 - The general rule of thumb is an inverter should be able to output 1.5-2 times the max draw of all your components. Assuming you will not power anything else, 1000-1100w would be ideal for the PC.
3 - Don't cheap out on an inverter. Cheap inverters are not only cheap in the monetary sense, they are usually cheap in the build quality and the components used. They don't last and are likely to cause problems.
That said, a quality 1000w inverter won't be cheap.
4 - Have you considered lowering your specs, specifically the 3D card? If you can reduce your power draw from the video by using the onboard video, you can use a higher-end DC-DC PSU like an Opus 320w or DSATX quite nicely, and not deal with the headaches of the inverter.
A "smart" PSU also has capabilities of turning the PC on/off with the ignition, which would eliminate the need for the DSSC that you mentioned.
5. Any device that's on when the car is not running will drain your battery, plain and simple. The greater the power draw, the faster it will drain the battery. Without measuring the power draw, it is impossible to say how quickly the battery would drain. The condition of the battery and how often you recharge it by driving also plays a part.