JSEvans' answer is mostly right. But There are still some things that I would like to point out:
First, creating your own VPN is way less anonymous than using public VPN or Tor, to the point I would like to assume it as completely NOT ANONYMOUS. This is because only you are using the VPN at a time, and that means any activities coming from that IP can only relate to a single person, in that case it is you. Adversaries might not relate this to your real life identity (such as approximate location if you don't use any proxy at all), but they are able to identify "You as you". On the other hand, public VPNs and Tor have a busy traffic. Many people are using it, so adversaries can only relate this address to a group of people that uses it.
Second, since there is only one hop in a traditional VPN, you have to trust your VPN provider (or hosting provider if you are self-hosting). This is because they know both your address and destination. If they get hacked or searched by an adversary, you are deanonymized. Unlike traditional VPNs, you don't have to trust your Tor relays. In fact, there are many malicious relays out there, namely exit relays designed to sniff non-encrypted traffic. You might be using one right now, but as long as your data is E2EEd in the first place, it's fine to let them record some encrypted garbage.
To sum it up, use a public VPN with Firefox, enable
about:config, and browse in Private Window might serve your needs. As long as the VPN is not blocked by the website, in most cases you should be treated as a different user every time you restart Firefox.
You might also try web proxies like the "Anonymous View" provided by startpage.com search, or the proxy from hide.me VPN through tor. Remember only browse publicly available content, and not sign in on those proxies, since the pages are actually MITMed by the proxy then presented to you.