I've run both Tekkit and vanilla / Bukkit minecraft servers, here's basically what it boils down to:
RAM: 1GB is fine on a vanilla server, with no addons/plugins, and up to 10 users.
CPU: Minecraft is VERY CPU dependent. It doesn't matter how many cores you throw at it (2 is about the maximum) due to the limitations of Java's runtime execution - at least until they add better SMP support. The faster your CPU, the better the server will perform. I've played with this one extensively - my Phenom II X6 1100T can't hold a candle to an Intel Xeon 2.24 GHz. The Phenom II X6 runs at 3.3 GHz natively, but the Xeon has a vastly superior IPC (instructions per clock) and does a fantastic job hosting several players at once. I knew the Xeon would be better since it's a server CPU, but I had no idea HOW much better until we loaded the server up and got several people going at once. It was night and day.
The other big factor to consider when hosting a Minecraft server is bandwidth. Ideally you want at least a 2 meg upload, with 5 meg being good for more than 5 people on at once. I recently moved, and had to get rid of my 22/5 cable and downgraded to a 7 meg down, 864 kilobit up DSL, and I can't host more than three people at once. It really, really sucks.
I have lots of hands on with this, so if you need any more help, don't hesitate to flag me down.