The question comes down to whether you're buying a computer for this year (only), or are you buying a computer you would hope to make productive use for for years to come? If the former, then a very basic computer should be fine. This year, you don't need super-deluxe video (because that's mostly for video editing and gaming). This year, you don't need more than 2GB RAM (because more RAM is most for complex analytical software and gaming). This year, you don't need to very best wireless adapter (because that's mostly for IPTV and gaming).
But who knows what you're going to need from your computer three years from now?
It is excessively unfortunate (for parents), though, that a computer best suited to withstand the changes in your needs and in technology that the future will bring, is also the computer that is best-suited for gaming today.
Personally, these are the minimum specs I'd aim for, looking towards the future:
2 GHz Dual Core processor (with 800 MHz bus)
4 GB RAM
250 GB hard drive
15" screen (not for word processing; for writing software, perhaps)
Wireless-N card
minimum 3 year, in-home warranty (I cannot overstate the importance of this)
I would also aim for a better than standard video card, and a DVD burner, so you can back-up data very easily (a tape or network-based backup solution would be even better, but a lot more complicated and expensive).