The first thing you need to know is that it's incredibly easy to overbuild/overspend on a computer for the purposes you describe. The next thing you need to know is that teenagers want to be online or on the phone at all times, preferably both, so dsl or cable internet is a good investment, along with a firewall/router to allow simultaneous net access from multiple machines, while leaving the phoneline free.
Now, check the hotdeals forum, see if there are any Dell Deals at the moment. They've been practically giving 'em away recently- there's little point in building your own if it costs significantly more than a good oem machine. It gives you a price reference point, if nothing else.
Matx systems are probably the way to go- they're smaller, cheaper, and lack nothing you want. I'll illustrate form a web vendor I've never dealt with, just as an example. Pair this mobo with a 512k cache retail p4 northwood-
http://www.z-buy.com/product.asp?item=MB-ARM266AG
Add 256megs of PC2100 ddr in an Inwin s506 (or any inwin s5xx series, depending on the vendor) case from the same vendor, and either a conexant or lucent chipset modem, if you're going that way. Forget separate sound and vidcards for the moment- your daughter probably wouldn't appreciate the difference. The Inwin case will accomodate a full size atx psu if you add a power hungry vidcard , extra hdd, or whatever down the road. Depending on how she uses the box, either a dvd or cdrom drive, floppy, liteon cdr round out the package, along with a retail copy of XP home.... and a single quiet 80mm exhaust fan, like a panflo L1a.... 17" monitor, I like the Samsungs....
Shop around for a keyboard/optical mouse combo, speaker choice depends on whether she wants to actually listen to music on the computer or just listen to the bings and bongs...
About 90% of all computer users would be thrilled to death with that box... well under $1K.