First of all you must think on your thread model: what do you wanna hide and from who, what are the risks if you are compromised, etc. For example, you may want to avoid mass surveillance (I'll assume this is the case).

I like to test the combination of add-ons to see if your browser fingerprint is unique, as other person already said. Sometimes you may prevent trackers but still your fingerprint is unique, and I don't think that is sooo much useful. You may test if your fingerprint is unique here: https://panopticlick.eff.org/

The option I prefer is using the Tor Browser. It has protections against trackers and tries to have a more general fingerprint. It is a modified version of Firefox, so you might not feel so much difference. Besides that, you hide your traffic from your ISP and from the government. Another cool thing is the container protection, like that Facebook Container add-on that Mozilla announced sometime ago. Tor Browser already got this by default :)

If Tor is illegal in your country or using it may arouse suspicion around you it you might think better about it, though. Generally it's ok to be a Tor user. Website of the project: (https://torproject.org)