Sure is a nice computer you have there, be a shame if something were to happen to it.
When you purchase a new computer, it likely comes with antivirus software and it sure looks good....
But most of the antivirus programs that come with a computer are on there so that you will buy a subscription later. Norton and McAfee are both reputable companies that do a good job of protecting your computer, but all antivirus systems have good and bad points, and my experience with both causes me to recommend alternatives. The first and biggest reason I don't recommend them is because you must pay for a subscription and people put that off and thus expose themselves to virus infections.
On that note, do not install a new antivirus until you uninstall the old one. Two antivirus programs running at the same time do not make you safer, they actually work against each other.
For most users, I recommend Microsoft Security Essentials because it is free, easy to use and reliable.
If that doesn't work for your needs for some reason, other free anti-virus programs include Avast, Comodo, AVG, Avira, and Panda Cloud.
Check out Kim Komando's security center for good recommendations. (I don't always agree with Kim's preferences, but her advice is never bad.)
Note that most of the products recommended as free are free to home users and are used to promote other paid products. You should not need to pay for any of them unless you're a business. Free antivirus for business is much more rare. If you absolutely require free anti-virus for business then consider ClamWin. It has a fairly high false positive rate in my experience, but it does offer alerts by email and centralized downloading functionality if you need it. I recommend using it with the option to unload from memory enabled, but not the automatic quarantine. Investigate any virus alerts with jotti.org.
I've had good and bad experiences with paid anti-virus for business, but here are some worth investigating:
Linux users don't need antivirus 99.999% of the time. The likelihood of getting a virus on Linux is probably about the same as having a plane crash into your house. Nobody will deny that it is possible, but the risk is low enough that preparing for it isn't really necessary. If you're one of the few that have a real need because you host files that are used by Windows users, then you can get ClamAV. It does a good job and is, of course free. If you've been hit by viruses a few times, it might be a good time to find out more about Linux.
Note that antivirus programs are not firewalls. You may need a firewall in addition to your antivirus software. Read my article on how to avoid getting hacked for more on the subject.