EA just released a 3 minute video that serves as a recap of what happened before Dead Space 3. It's a refresher for the people who need one. But for those that haven't touched the first two games, major spoilers ahead.
A demo for Dead Space 3 is scheduled for January 22. If you own an Xbox 360 though, you can opt to get the demo a week early. Getting it a week ahead is nothing special, but if you really really want to be the first few players that have played Dead Space 3 before it hits retail on February 5, register away.