Most XBox360 games wont need the HD , most XBox360 games wont need cache because of the fast DVD DRIVE.
XBox games will need HD but MS is helping upcoming XBox games to be made to be compatible without HD in XBox360.
HD is needed for LIVE , Content , Marketplace , you can use a Memory Unit but you wont be able to get a lot of content in it.
If you buy XBox360 Core you can later buy a 20GB HD for $99 , but is best to buy XBox360 cause it comes with HD and much more stuff saving you a lot of money.
Plus you will be able to download stuff into the memory unit from stores that have a kiosk , you can plug it , download new themes , trailers , saves , new content and then trasnfer them to your XBox360 console.