> I currently have no VPN or other privacy protection measures.
In most cases a VPN will not provide you privacy, contrary to what others say and marketing ploys. Your habits online are not any more anonymous than your ISP connection. Using an encrypted DNS and HTTPS will give you security. 'Privacy' and 'Anonymity' are often used used interchangeably. You should know what you want.
VPNs are useful if you want to hide your traffic from an ISP. Your ISP can still see you're connecting to a VPN. A VPN can also provide ways of downloading content without getting a anti-copyright notice. You're putting your trust into the provider, and that is inherently a problem in itself. Tor in addition to using
Tails or
Whonix is ideal. Whonix is a lot more savvy in setup while Tails is not.
> Could I possibly get into trouble for using this website?
No. There is nothing illegal about this site. There is nothing illegal about discussing suicide or reading up on methods. Walking someone through their suicide could potentially cause legal problems. This is against the rules of the site, anyway. Keep things on this site and you should not have problems. The site administrators have a lot of protections on the end-users to keep their information secure. In addition you should practice OPSEC, too.