Depends how how many games you play and do you download downloadable content (DLC).
For example, I have an older XBox 360 with just 20GB, but I get by because I usually just play one game at a time. It is recommended to "install" your games to the HD for faster load times and less noise, so that requires about 6-8GB.
Also, do you like to try out game demos? Those are usually a couple of GBs. Do you plan on buying a bunch of XBox downloadable games? The XBox arcade games are usually under 1GB each.
Do you plan on downloading movies and music to your hard drive?
If you answer no you most of these, you can even go the barebones route and get an XBox without a HD (arcade model) and just buy a 16GB flash drive to store your content.
If you answer yes to a lot of this stuff, then bigger is better.
But it really depends on how many games you wish to have access to on the hard drive (demos, installed games, DLC).
BTW, you might want to check out the newest model Xbox called the XBox 360 Slim. It only cames in one HD size, so it makes this question moot.
Best Answer
Officially, the Xbox 360 only supports using Microsoft's official Xbox 360 hard drives. These are basically laptop hard drives in a special (Xbox specific) enclosure. Using a standard hard drive is not a supported scenario.
You could buy a USB enclosure and connect your hard drive that way, however you'll only be able to use 16GB of the drive (that is the maximum size USB drive the Xbox would support). I think that you can have multiple USB drives connected, so you could in theory partition it into multiple 16GB partitions and see how that works.
If you want an Xbox 360 with a hard drive, I would suggest buying the 250GB model, since this is generally cheaper than buying the 4GB model and a 250GB hard drive.