Downloading BitTorrent itself will likely not give your computer viruses. If you are torrenting massive amounts of data from BitTorrent then yes you put yourself at risk for getting a virus. However, you don't have to pay for virus protection! I suggest AVG free or Avast! antivirus programs to over some minimal protection and scans if you are going to be doing this. Honestly there is no guarantee that you will or will not get a virus, but by running AVG Free Antivirus or Avast! you will greatly reduce the risk of getting infected
However I have to warn you that if you do not pay for music, your Internet Service Provider may contact you and threaten to cancel service if you continue to pirate copy-written music or videos. Essentially how it works is that they as an ISP can get in trouble if you are doing so and then will threaten to cancel service to comply with DMCA laws and answer to other authorities - they will sometimes watch what you are doing with this.
Installing Linux on your computer will not guarantee that you will not get an infection. This is a myth and it is possible that you can cause issues on a Linux system, but it is MUCH less likely that you will. I would honestly avoid that learning curve overall.
