I just took a bit of a look around, and a lot of people have said the main part of running a Minecraft server is the internet connection - which sounds about right, especially if it hosts around 15 players.
This is also something I'm interested in doing, and i would like to point out that my old computer had an Intel quad core processor, at 2.4Ghz, and was fairly recent (after Pentiums but not as new as the i3), with 3GB of ram, and some integrated Nvidia graphics - and i could barely run Minecraft for myself, let alone for 2 people, when i tried that.
Here is what the Minecraft Wiki says:
Quote:
Running inside windows (Non-Dedicated):
2.8Ghz Dual-Core, 3GB RAM (XP) / 4+GB (Vista/7), A High-Speed internet connection (10MBp/s)
Running on a *nix Based Server OS (Dedicated):
2.2Ghz Single-Core, 2GB RAM, A High-Speed internet connection (10MBp/s)
The requirements for Windows can be dropped slightly if you are NOT going to be playing Minecraft on that machine!
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Being a wiki, i wouldn't take that as an exact guideline, but it is good for a general idea