1000H uses Attansic Technology L1E lan and as far as I know there is just some experimental support for L2 and no support at all for L1. I'm using a 900A (Intel Atom), same Lan but Atheros wifi (I have to use stable together with ath_hal from current). Asus 1000 != 1000H, Asus 900 != 900A and so on, it's a silly game but they are using different hardware setups with every revision.
To get FreeBSD on some EEE follow this howto,
http://bsdimp.blogspot.com/2007/10/b...86-images.html
I have got working HDA sound, graphics, standby, but I have some severe problems with my card reader. If you don't want to tinker a lot, take some Linux distro _at the moment_.