I use only Chrome and IE9 (I don't like IE but some of the websites at my college will only work on IE9), so I'm not as familiar with Firefox. If you want to be extra secure though, there are some nifty Firefox add-ons. One of them is
Better Privacy and another is
Ghostery. They each have similar functions, however, Ghostery gives more detailed information, such as it will show each tracker on a website. This can be very useful because you can selectively block each of them. Better Privacy is aimed at LSO cookies (think of them as cookies that are harder to detect).
There probably are other add-ons but those are the two that I know of.
An alternative to all of this is to just use a VPN. If you want to be extra secure, you can connect through a proxy server to the VPN, although that is probably unnecessary. A person can still track your laptop even if you use a VPN with or without a proxy, but it's not going to be easy and most websites aren't equipped with the proper coding to do this.
You can also connect to an IP server in another country but this can be a bit dangerous as you have no idea whether they store any data on you. On the other hand, VPNs will show whether they let other websites track you (btw, they don't because that's the whole purpose of them).
Unfortunately, I'm not well-versed in using Android phones but I'd imagine adjusting the settings would be similar to a laptop or desktop. I have a few friends who know more about them as well as Java ME ("form" of Java used for developing apps), so I'll ask them if they have any other tips for using Chrome on your Android.
You can also try
Maxthon (different Web browser, mostly for Apple) but also works on Android. I've never used it so I cant say how it is.