What you really want for privacy & anonymity are anonymizing proxies, which are not mutually inclusive with VPNs. Proxies work best at the app level, not network level. Proxies can also be located anywhere and hide your request origin, and your browser can even forward DNS requests through them. But to strip every inch of personal information out of HTTPS traffic you may need to accept a custom CA, which reduces your security. So use a VPN for security, and proxies for privacy & anonymity.