First off you'll need to select your Linux distribution (distro), I shalln't advise on that because I have far too little about their variants. All I will say is that it might be best to go for a comand-line OS, rather than a graphical one.
For a CPU, it seems the average is around the 2.25Ghz mark, although it you want to be sure it'll be good for years to come, then you might want something in the region of 3.2 to 3.5Ghz.
If you intend supporting high volume traffic then you're probably gonna need a fair bit of RAM too. Maybe about 1 to 2 Gb of ram? I think the sort of ram you need for sticking in a machine running web servers for high volume (can't remember its proper name but it doesn't leak memory all over place like standard RAM does) costs quite a lot. I can't remember if it is around $1000(usd) or $10,000(usd) for a stick and if that stick would be a 0.5Gb stick or a 1Gb stick.
The ammount of storage space required (size of yer) HDD's will depend largely on what your site does. If it is just the sort of site that dishes out info without recieving much. Then you won't need a vast ammount of space. However if it's a commerce sort of site that is constantly taking in info (users account storage, order details, order progress etc etc) then you're going to want to start big and get bigger.
Oh and of course, you'll need a monster sized internet connection.
Sorry for the pretty vague info, but I don't really know much about your requirements and hardware is not really my thing.