First of all, definitely avoid Kazaa or the FastTrack network. Kazaa itself is a source of all your spyware, and most files on the FT network are fake.
The Gnutella network is so-so, but you can still get viruses, so it helps to be more aware. Don't download any unknown executables (.exe) and zipped or rarred files (.zip or .rar) because that is where mostly all viruses are contained. Some spyware may also be in those files.
.mp3 and .avi are alright, because it is hard to bundle scripts into those formats. If a .wmv has protected content, or a .wma, close it immediately. It will mostly infest your computer with insidious spyware.
When in doubt, upload to this site: http://virusscan.jotti.org any of the executables or zipped files you've downloaded. It will scan those files and check if they have viruses so that you can be sure even before opening those files that they are clean. Note that they have a 10 Mb limit to upload, though, but it's enough considering most applications are less than ten Mb.
Now, back to the question. http://www.frostwire.com, the FrostWire P2P program is clean, free, and fast. That should be good enough for your needs. :)