The Arcade is backwards compatible. There is a list of games that are backward compatible, and not all XBOX games work on the 360, and some do not work as well as if run on a XBOX. Also, the Arcade has no HDD. I am not sure how well a memory card would work. I think you will be fine with a $299 20GB 360 for the time being. I'd be surprised if the XBOX memory cards work on a 360, although I really have no idea. I've read that a GamerProfile can be stored on a memory card, but I think you're better off with a 20GB or 60GB HDD.
RROD is not caused by the HDD, it is caused mostly from overheating and the 'X-Clamp' failing to hold the motherboard up. Google 'X Clamp Fix' to get a better idea of this aspect of the 360.
Also, you said you don't like to pay full price for games, and since you play a variety of platforms, I recommend GameFly's online rental service, since they offer a variety of games from a variety of systems and would fit your needs very well, I think. I use Gamefly currently, and occasionally buy games from them for much less than the retail price. I currently use the one game at a time plan which is $16 something a month, IIRC(If I remeber Correctly)...
