Ok well you can do this two ways then:-
1. Start creating the site. If you do or don't get any icons you would have still learnt about making sites and would have gained something at least. Its likely though that if you don't get icons fairly soon you will lose interest.
2. Wait until you get a source of icons and then develop the site. Keep in mind you can't just copy them off another site. You either have to get them made for you, make them yourself or find somebody who has made some free to distribute.
Either way you will want some sort of dynamic site and ideally connecting to a database to keep track of all the files. A quick thought I had was that you could use something like this:-
http://gallery.menalto.com/
Its a photo album software, but theres no reason you couldn't use it for an icon site to just get a rough idea whether your idea is feasible. It has the 3 main areas that you require:-
1. image upload
2. Image preview
3. Image download
Then when you have a more precise idea about what you want, you can either look for another piece of software that best matches what you are looking for, or get/pay somebody to write it for you.
To get it up and running you will need a web host with PHP and MySQL, I'm guessing you will be looking at around £5 - £10 a month for that. Alternativly, I can set you up with some free space on my server here at home. I can't guarantee 100% uptime every month, but for testing it should suit you fine.