If one was able to get just about any totalled car for a cheap price in order to part them out (on ebay, etc.), what cars would be best to purchase? Ones that commonly break down, are popular, etc. Any help is appreciated :)

I would suggest ones that a whole bunch of people have. You standard family sedan would be a good answer. For body itself, think of the cars the insurance company wouldn't let an 18 year old male drive, and that would give you an answer.