Iceweasel is Firefox by another name (the puritans at Debian won't use the name Firefox because it's a protected trademark). There's Konqueror from the KDE camp, that quite nice. Epiphany is more for local browsing of directories. Never intended as an everyday browser, although expect to be corrected! Chromium is basically Chrome, but fully open source and packaged by Debian maintainers.
The trouble with picking up binaries from the internet, and installing them, even from people like Google, is that they won't be routinely updated. By just issuing the following command, all packages in a Debian system with available updates are retrieved and installed, but only if you installed them in the first place through apt. Software installed by downloading packages or even raw binaries won't be updated.
$ sudo apt-get dist-upgrade
Chrome has probably got some spyware in it that will secretly phone home periodically. Ostensibly to check for updates, but in the process apparently telling Google about your browsing, etc! So far as I understand it, that was largely the point of Chromium, to seize back control of the Chrome browser.
There are probably loads more browsers to choose. I'm happy with Iceweasel (Firefox). It handles everything I throw at it, and rarely crashes, but then I'm no power user.
Did you try out the email clients? The Evolution client has come on leaps and bounds. It even works with Microsoft email servers these days!
cheers, a
EDIT: It looks like Google does add itself to the source.list of apt, so updates to Chrome should be retrieved along with other installed packages.