Is an anonymous VPN (like frootvpn) all I need to remain anonymous online or do I also need to use TOR or take other measures?
In general I'd say you need to do more than just use a VPN.
What VPNs do:
VPNs solve a couple of fairly specific problems:
Your local ISP (Internet Service Provider) and network provider can see all your unencrypted traffic. This could be groups like your school, work place or whoever is running the WiFi at your local cafe. A VPN encrypts all the data between you and the VPN end point so it solves this problem.
When you connect to a website they can see your IP address, often all the computers on a network will use NAT (Network Address Translation) to share a single public IP address. So if your laptop, PC and Mobile are all connected to your WiFi they will most likely share a single public IP address that could be used to track you. When your trafic goes through a VPN the website will see the IP address of the VPN instead of your home.
What VPNs don't do:
While a VPN will encrypt your traffic and hide your IP address the main way people are tracked online today is through cookies in their web browser.
Companies like Google and Facebook will places a tracking token in your browser that is sent back and forward between you and them every time you view a page that has Google Ads or Facebook Like buttons.
However tools like that don't hide your IP Address or encrypt your traffic, so they can be complimented nicely by using a VPN.
How to browse anonymously
With a combination of a VPN and selection of privacy tools it's possible to remain repetitively anonymous online.
However rolling your own solution is hard, and it's easy to make mistakes where a single mistake can undo all of your effort.
If you want serious anonymity online I highly recommend checking out Tails it's a pre-built Live Operating System bundled with everything you need.
 Or if someone malicious is monitoring the traffic on that WiFi or network.
 There are large database that map IP adresses to approximate physical locations.
 or whatever network your on at the moment.
 Here I'm thinking for average people not nation state actors like the NSA.
To be honest, I think the BEST ANSWER can be found here: Best practices for Tor use, in light of released NSA slides
This guy details /everything/ in so many ways.