Yeah, it will handle media just fine. I'm assuming you'll be streaming from network storage. I'm also assuming you are aware how slow the E-350 is with duties other than media playback.
Here's my own E-350 build if you are interested:http://s179.photobucket.com/albums/w319/rwpritchett/HTPC/HTPC%20Nirvana/?start=all
I have my own E-350 Netbook and I love it! It will not stream media, but it will be for my grandpa and he isn't gonna need more than 20 GB IMO since he will only be storing around 1000 pictures on it (No games, or movies).