Number 1. NEVER EVER EVER EVER EVER log on as root / any power user!
Compromised processes running as root will be able to modify system files. This is why windows users get stung with virus' and spyware. When the browser is run, it inherits the power and can then install the nastys.
This is the same in linux
Also make sure your sources for updates are decent and you watch what you download.
Also make sre your operating system is up to date by running
sudo apt-get update; apt-get upgrade
This way it will be as secure as possible. Also reducing the services your system runs will not only make it faster but less like ly to be compromised