I'm far from an expert, so take what I say with that in mind.
A VPN (Virtual Private Network) requires software, probably provided by your VPN company, on your end and software on the end of your VPN provider to create a "private" internet connection between the two. Once you've connected they have become your ISP. As such they MAY keep records on your surfing activities.
Tor is a browser that routes itself through locations around the world when you open it. This browser looks very much like Firefox on which it is based. The sites to which you negotiate cannot track your IP address. (I also don't know of any services that are free, but there may be. I used Witopia for a while and their tech support was available 24/7 via chat. They were quite helpful and responsive on the few instances I needed a question answered.)
So, given this, you might want to use both a VPN and Tor browser if you're in need of privacy and/or non-trackability.
One of the problems with Tor is that these worldwide connections will probably mean your browsing will be slower.
I've also heard that the NSA can hack Tor. Good luck.