Definitely stay away from Limewire. Nearly every song that you can download from it is pirated. So downloading them would be theft and would put you at risk of being sued by the RIAA (although the odds are very miniscule). Also, as the others have mentioned your chances of getting viruses from files downloaded on Limewire is rather high.
You are much better off buying CDs or using one of the legal download sites such as iTunes. Whichever site you choose you should be careful to understand what you are getting. Some sites, such as Napster, offer unlimited downloads for a certain price. What they don't make clear is that you have to pay each month in order to keep listening to the songs that you download. As soon as you stop paying the monthly fee, the songs no longer work. There are also restrictions on what you can do with those songs. Even while paying the monthly fee, you won't be able to write any of those songs to a CD or transfer them to many mp3 players including iPods.