Any reason why you want external?, as these are more expensive than internal - however, they do have the advantage of portability.
I haven't any direct experience with external hard drives, I guess its very much like the internal choice and down to personal preference.
Do a search via google for more information - many of them seem to be firewire or USB 2.0 - neither of which may not be suitable for your daughters machine, unless she has firewire access or USB 2.0 ports.
If not, you need to be looking at the USB 1.1 versions. Another thing to consider, is the hard drive needed for program installations, or because your daughter has many saved files and data?
If its the latter, then a CDRW may be the cheaper and better option. She could then back up her files to disk and delete them off her computer to recouperate disk space.
I hope you find what you want, and happy birthday to your daughter :)