What security software should be installed on a Linux machine connected to the Internet to ensure adequate protection?
Also – is there a risk of propagating viruses from Linux to Windows ?
use SANDBOXIE to trap all viruses ....
Regarding viruses crossing from Linux to Windows, or vice-versa:
There's also such a thing as a firmware virus - Stuxnet was the first of its kind (although I've seen firmware viruses beginning in 2008/2009). Basically, the programmable logic circuits on almost every hardware component have enough storage space to contain viruses. These are OS independent (although Stux required Windows to spread initially).
So basically, some viral infections can persist even through an OS reinstall.
Regarding cross propagation, viruses written in Java will work across platforms. There haven't been many in the wild, but they're not unknown.
Any machine connected to the internet should have a firewall. The exception to a firewall on every machine is in a larger networked environment where the IT group will generally provide the border controls (firewalls for the entire network so a host-based solution is not required on every machine providing for a single point of control for access to the internet as well as to any appropriate machines on the internal network, such as internal mail servers or a web server in a DMZ).
It is possible to pass a virus from one OS type to another. It is extremely rare for a single virus to be able to effectively infect both types of OS. I have seen two different sets of proof-of-concept code that will sometimes work on both systems. The most effective way for this to happen though is with a dropper that detects the OS of the current machine and then it downloads other malware based on that information that will do the heavy lifting of trying to drop a payload.
Overall, if you want to make sure you are playing as nice as possible with Windows computers, you should run ClamAV or another antivirus package on the Linux machines just so they will not inadvertently pass along a Windows virus to those machines.
Avast is the best Antivirus -
Yes there are viruses that will affect both linux and windows, just not very common in the wild.
I have AVG installed on my linux box, but Avast has a AV solution for linux worth looking at.
Also a firewall is something you would want to look into, I use Firestarter but there is probably a newer, better software firewall out there