Every computer connected to the net
should have a firewall. Whether you need one (a different one from that within Windows) depends on your particular computer usage. If, for example, that were to involve any activity, such as banking, that could involve the loss of money if data fell into the wrong hands, I would consider a two way firewall a must.
Windows XP (SP1+) contains a very good one way firewall. It will stealth your ports, block unsolicited inbound connection attempts.
The difference between it and a two way firewall is that with two way you have outbound connection control. So if you were to unintentionally download something nasty, hopefully the firewall would alert you that something unknown was attempting to connect, and you then have the option to block it, and investigate the cause.
The weakness is that there can be quite a few legitimate processes, needed and sometimes un-needed, that it is safe to allow outbound connection for. By the time a user has allowed about two dozen of these, pop-up "fatigue" may settle in, and the habit may become to simply allow anything. Some firewalls (usually those with more user control) provide more popups than others. One of these firewalls in front of a jaded and semi-ignorant user, with the inappropriate rule allowed, can (ironically) end up being worse than just sticking with the basic Windows firewall. Much worse. (The Windows one isn't bad, just limited.)
Avast 5 will have a Pro version with a firewall included as part of a suite. There will also be a free Avast AV without the AV, and a Pro AV - only.
I would suggest you learn a bit about what might represent a potential vulnerability in any security/privacy protocol you might consider installing/applying. (As part of that, it would be a good idea to set the email address in your profile to "hidden", to reduce the risk of having that address spammed.)
A layered defense is a very good idea. I'm no firewall expert, so have chosen an applications-based firewall that is quite easy to use. (As opposed to a rules-based on that needs a bit of expertise to set up safely.)
Perhaps the most important rule to any element of the defense is to make sure you have a basic understanding of what each layer can and cannot do; what it is supposed to achieve.
Following basic research, this forum is an excellent place to ask for advice on anything you are contemplating. I've learned quite a lot here.
Welcome to the forum.