1 computer? Is this the dark ages?

With the amount of devices in the home with online capabilities, a wireless router is pretty much standard equipment these days. Having said that, if you don't need one there's no point purchasing yet.
I thought XP Firewall could be switched, maybe I'm wrong, it's been a while. Either way, as long as it's on and your anti-virus and copy of XP are kept up to date you should be fine. ZA is the only 3rd party Firewall I'd use, but it always seemed to misbehave with age and the number of applications grew. That's why I binned it, but then I was already behind hardware.
I'm not a big fan of AVG, prefaring Avast, but there are many who prefer AVG to Avast. Try them both and just pick whichever you prefare. Both are as good as retail products, with the possible exception of NOD32.
Follow this link to see how secure you are. The site will fire packets at all the usual ports to check your security. There's plenty of info on there too for tips and advise.