OK here's what you'll need to know:
The Xbox 360 has the ability to run games directly off of games or to install the games - when the game is installed, the console will require you to insert the disc (to verify that you actually OWN it) but it will load the game content from the harddrive as opposed to the disc; the benefit with this is that the HDD is the central data hub for the console so it's content is right there, but the disc would require the optical drive (DVD-ROM Drive) to load the content from the disc and then send it to the HDD to be loaded.
Benefits to this: Faster load times, quieter console, cooler (temperature) console
Most games tend to be anywhere from 3gb-6gb
Also, if you plan on installing demos, lots of dlc, movies, music etc. keep in mind that each demo is roughly 300mb-2gb - so that will fill up your unit FAST.
Another note to consider is that you won't be getting the FULL 4GB - it's more like 3.5 (as the console itself has stuff installed on the HDD)
Some games (released BEFORE Xbox 360 S [the newer line] was released) won't consider the 4GB HDD as a HDD because there is still an unnused harddrive slot in the unit - games like Halo: Reach will not let you play Firefight and Campaign over Live Co-Op... as far as I know though, this error was fixed for Reach in the latest update as well as many other games.
If you REALLY want more harddrive space, you could always just plug any FAT32 HDD (plug-and-play portable harddrives or flashdrives) into the Xbox 360 and go to "Set up for Console" (or something along those lines) and you'll be able to use this portable drive as a harddrive - the only downside is that it does not take care of that error I mentioned above. However, you can still install games, dlc, movies, music and additional content to your FAT32 drive just the same.
If you still want to use an internal HDD (a bit faster than the FAT32 connection and no known errors for pre-S edition consoles), you could just as easily by the Harddrive for the original Xbox 360 consoles (the harddrive would be grey) and just open the case and drop it right into the top of the unit; this is a MUCH cheaper solution to the harddrives sold specifically for the S models.
What I did when I upgraded to the S models:
I used a 320GB FAT32 harddrive to store most of my movies, music and installed games, and then I took my old 20GB harddrive from the old models and dropped that in (this was done to prevent any possible errors and to install games like Assassin's Creed, Halo Reach and Tekken 6 DIRECTLY to the console).
Hope all of that helped!
