I'm about to build myself one for the same purposes, I will tell you how i think im gonna make it.
I might go on and install Debian on it, and configure everything properly using Samba, but i have been looking after Windows Home Server 2011, and it has pretty cool features.
1) I got a Core 2 Duo E8400 with an Matx ASUS board, thats what im gonna use.
2) For a case, a small one, i have been looking at some matx cases fractal has, they are pretty cool, and look really good.
3) For CPU cooling I will use a low profile silent air cooler, as the cpu wont be under much stress, the most cpu intensive thing might be streaming video.
For Case cooling and Hard Drive cooling, i will use some really good, silent fan which undervolts well, i still dont know which one, but I want it to be really silent.
4) For Hard Drives, I will be using WD Red's, those are pretty good, close to enterprise grade hard drives, designed to run in RAID configurations.
What I still havent decided.
5) If I'm using RAID 5, 6 or 1, yes 1 might be an option
6) which RAID card im going to buy.
7) If I'm finally going to get an Intel lan card, and use that feature that allows you to run multiple cables and create just 1 connection with them, getting for example a 4gbit link (max)