You don’t need Linux to torrent. The VPN is so your ISP doesn’t send you love letters. That’s the useful thing. Once you have a VPN, there’s no reason to be paranoid about conventional piracy behavior.
If you’re paranoid anyway, it’s more than just your choice of distro. OpenBSD is kinda made for paranoia, but you still have to think about who you’re hiding from, how much is at risk if you get caught, how much time and money it’s worth investing to protect yourself, what threats you’re up against etc. Like, are you more afraid of downloading malware or being caught breaking the law?
If you just want some movies and music, get a vpn and go nuts. If you have no vpn, you can avoid being noticed by not sharing stuff that’s popular when it’s popular, like blockbuster movies.
Tails is a USB bootable linux distro folks use to buy drugs, FYI. Tor is helpful for staying anonymous from some companies and governments. I2P may be more private than Tor. Like, if you’re afraid your government will put you in jail for political beliefs, then you start looking at in-depth OPSEC.