Given your girl is still little and she will be treating the computer a bit roughly, you might want to go cheap and get a second hand case. That being said...
Athlon 64 3200+ Barebones Kit with Mainboard CPU RAM DVDRW More!
Athlon 64 3200+ Barebones Kit w/Mainboard, CPU, RAM, DVDRW and More! 10-Bay XG Sidewinder 2 ATX Mid Tower Case Features:Black with Silver accentsIncludes 450 Watt power
ATX Mid Tower caseSidewinder Snake Logo (slides down to reveal I/O ports!)Case Material: 0.6mm steel
MSI K8N Neo V2.0 H nForce3 250 Socket 754 ATX Motherboard Features: NVIDIA nForce3 250 chipset Socke
AMD Athlon 64 3200+ Socket 754 CPU Features: AMD Athlon 64 3200+ CPU 2200 MHz frequency 1600 HT spee
Price:$209.00
There's no way you need a case with 10 drive bays! Unless if you want to use it to store lots and lots of video files. Other than that, the specs seem fine. But ask yourself what types of games she plays though, because the video card might be overkill.
FX22/VIA K8M8900CE/AMD Sempron/athlon 64X2/4-DDR2
Shuttle PCs are nice and compact, but you pay a premium: prices can be a bit more expensive, and expandability options are limited. But if you don't want to be adding any extra hard drives or anything, this shouldn't be too much of an issue.
I've had good results with Pricewatch.com and Newegg.com for buyin computers and gear. No advise about barebones kits. All I'd recommend is getting a software like Norton Ghost and creating backup images of the hard drive very often. Oh, and don't get an LCD screen - for some reason, little kids and LCDs don't get along very well.