A 4gb average is probably a better bet, and some games can go a fair bit higher then that. 200gb will probably leave you wanting, as a drive's total capacity is usually referred to in "manufacturer's megabytes" - really you'll only have ~185gb worth of usable space, and about 8gb goes towards the X-Box's reserved partitions, so you'll really want something bigger.
Also remember that, if you've already got your fifty discs ready to load onto the system, the drive will be filled as soon as you're done backing them all up. Meaning that if you collect just a few more discs, you'll need to upgrade the HDD again.
And then there's the possibility that you'd want to load other media onto the drive, such as videos, images, music, emulators, etc...
In short, data is like a gas - it expands to fill the space available. Getting a bigger drive only delays this process somewhat. Personally I'm running a 750gb drive, it's full, and I'm considering a 2tb for the next step up.