Ubuntu has a firewall built into it (just like all linux versions have) but it's disabled as default and to be honest, as you're almost certainly running it behind a router I wouldn't bother enabling it (if the computer was directly on the internet then you'd definitely need to enable it)
If you really want to enable it for any reason install GUFW from the software centre (if it's not already installed) and then look in system > administration for firewall configuration.
I don't bother with running antivirus all the time but I do have a command line scanner installed purely for scanning suspect files before letting them anywhere near a windows computer.