I recommend that you use Firefox for your Internet browser and Thunderbird for your e-mail application (or use Internet web e-mail). You may want to run the Chromium browser also, and I recommend that you set it up with similar restrictions as Firefox. However, the specific add-ons that I recommend for Firefox makes it the better browser (for privacy and security) in most situations (in my opinion). Both Thunderbird and Chromium are available from the Ubuntu Software Center. A number of plug-ins or extensions to Chromium may compromise the integrity of its "virtual machine" ability. Therefore, I recommend that you only install plug-ins or extensions that do not require access to computer system resources outside of Chromium itself.
If you decide to install Chromium, I recommend that you setup Options → Personal Stuff to not remember passwords. Also, in Options → Under the Hood, disable the following: 1) "Show suggestions for navigational errors," 2) "Use a suggestion service to help complete searches and URLs typed in the address bar," 3) Use DNS pre-fetching to improve page load performance," and 4) "Enable phishing and malware protection." These services are actually Google services, and even though they are helpful in a number of ways, they may compromise your privacy. Read Google's privacy statement to make your decision. Regarding the DNS pre-fetching, if you set up your computer and hardware firewall as recommended on this website, the DNS addresses should resolve so fast that DNS pre-fetching becomes an insignificant performance factor.
If you want greater privacy, use Firefox as you Internet browser and set it up as recommended in the link below.
I also recommend that you be very careful about installing extensions, add-ons, or plug-ins to either Firefox or Thunderbird that are not recommended on this website. (Some also come pre-installed with your Ubuntu installation, such as in Firefox. These are fine.) Fully investigate them first. Some add-ons may actually be spyware or have a spyware component, or they may cause Firefox or Thunderbird to become unstable, or cause some other kind of problem with other programs that you run on your computer, or cause a security venerability that could be exploited.
Click here for discussion on how to setup Firefox to protect itself and for privacy. Click here for discussion on how to setup Thunderbird to protect against viruses and malware---even though it will probably be next to impossible for malware to infect Ubuntu Linux and very unlikely to infect either Firefox or Thunderbird, which ride on top of the Ubuntu Linux operating system. For some websites, you may wish to use the Chromium browser (which offers good protection), although it may not give protection as great as Firefox when configured as I recommend in the instructions on the setup of Firefox.