I would definitely install an antivirus software such as AVG or Avast. Also, install MalwareBytes and Spybot just in case you need it when spyware strikes. If you access the Internet via a wireless router, change the settings so it's not using any default passwords.
Backup is another thing. Dropbox offers free backup up to a certain amount of storage. It's great because you can access your files from any computer with internet. Carbonite offers much more storage, but is strictly backup (cannot access files anywhere else). Good for media (pictures, videos, music).