officially, only official microsoft xbox 360 hard drives are supported but you can easily find tutorials to use your own HDD or buy preconfigured ones online at cheap prices.
and using these custom hard drives do not get your console banned
In short, yes, you can put any size HDD on the top of any Xbox360, and even swap them around between consoles if you so desired.
If you're going to try replacing the insides of the HDD though (say, for a 250G HDD), you'll need certain drives (mostly Western Digital) with a certain type of format (FATX if I remember) with a special little piece of code to make it look official. And a Torx6 screwdriver/bit to open it up, although based on your question, you're only thinking about official HDDs so this doesn't matter