Get rid of anything more than what I did in the video, and expect the car to fold up like paper in no time flat.
It will literally bend around you, as it was mine was already splitting at the seams all over the place, and the A pillars both split from stress. :o
Personally, I'd leave the panels, doors and anything that could add rigidity, bin the windows, trim and basically anything else that doesn't make it run, then brace everything. Do consider a roll bar seeing as the roof has all the integrity of a coke can.
*protip* leave the door rubbers on, it'll rattle like a bastard and drive you nuts after a very short while.
Even with all the extra bracing it'll be light enough to go anywhere, just have some half decent tires on it and you're set.
Oh, it's not very often I'll say this at all, but in this case a weldy is your friend.
*ninja edit* Wear a helmet, the little bolt that holds the seatbelt in place next to your shoulder is directly in line with your head in the event of a sudden stop while traveling sideways, I have a decent dent in my helmet from exactly this, and we're talking hospital time if you try to shift that bolt with your skull. Just something to keep in mind.