I use a VPN to connect computers together. Mostly for automated offsite backups of a few files.
In the past, I've used a local proxy app. This is software that runs on the computer that you are using and most internet traffic flowed thru that proxy software so that you can filter/block some types of traffic as well as some websites.
What it sounds like you would want is a VPN that runs between your computer and a server.
When you ask to see a website...
...your computer sends the request to the server inside the VPN tunnel
...the server gets the website
...and sends it to your computer inside that same VPN tunnel.
Getting webpages that way makes it a bit harder for those offering the webpage to know where you are.
While all of this sounds good/safe, lots of web-servers will not accept traffic from known proxy servers. So you will not have full access to the internet. Most forums that I've ever been involved with block proxy users.