fo3nix get their before me with the limewire info :)
I have limewire installed and it doesn't slow my computer down at all, though I done it the same was as fo3nix suggests
When you setup the computer and it's nice and fast don't install everything in one big hit, install one thing use the computer for a little while until you satisfied it's all running ok then install the next thing, then you should be able to see whats slowing it down.
Also whenever you install anything look at the install options while your doing it, a lot of software will try to get you to install other things that you really don't need, for example a lot of stuff will try and make you install the google toolbar, you don't need all this rubbish and it will just slow your 'puter down. They will normally have the box ticked by default so take the tick out of the box.