If it's only 3 months then you probably shouldn't bother with too much bureaucracy. It'll take you up until you leave to get it all sorted out completely legitimately. As Stravinsky mentioned, it's pretty much a long holiday, not residency - so no reason to get a residency card, right?

Are you planning to buy a car? You should consider contacting some of the larger rental agencies to see if they do long term rentals. Otherwise, take yourself directly to a sales lot and they will help you sort it out better than anyone else (they're extremely motivated, right?).