Paul,
I reccomend you go over to Steve Gibbs website and take a look around.
http://www.grc.com/default.htm
You should do the Shields UP probe test, this will test your Router/Modem and tell you how well its doing its job.
Now even if you recive a stealth rating for all ports on your Router/Modem, you still need other protection.
Look at it like this.
1. Inbound Traffic, A door to stop ousideters getting in. A stelth door just means that it will be invisable. A closed door is still visable and people can try to get in. An open door...
2. Outbound Traffic, A door does not usualy block outgoing access. But a good door can allow certain people out and keep others in.
Most good NAT based Routers today will give you a stealth rating.
However they will do nothing to stop outgoing traffic. One of Steve Gibbs earliest test was to let you download a small program to your PC and run it. It would then establish a FTP connection to a server and state you failed the test. But of course you want to be able to connect to the outside world otherwise whats the point of having access to the Internet. For example connecting to Iceinspace forums clearly shows your Router does not block outgoing HTTP traffic. But this is be design.
The question is controlling what on your PC is talking to the outside world. Is it being intitated by you or automaticaly on your behalf, worse still is it running without your knowledge for a malicious purpose. Usualy this is called a Trojan, as the refrence to a gift you recived that opens your doors to unwanted guests. Imaging you get an email with some innocent looking attachement. You run it and its some silly animation, but in the background it establishes a http connection to a website of its author, and uploads your personal information. Or downloads further instructions of malicious programs to be run on your pc.
An email from a trusted friend, which is actually not from him but from a Malicious program that has infected his system and automatically emailed everyone in his address book... You open it because its from your mate.. you click on the link or run the attached file and then your infected and your contacts get a nice email from you.
So there are many things to consider.
1. A good router should be tested by Shields up to ensure you get A stealth rating. If not consider a firmware upgrade or replace it. Infact Steve is now recommending two NAT Routers are better than one but thats beyond the scope of this.
2. A good per application firewall on each of your PC's, ok this is not really neccessary but this will ensure you know when something on your PC wants to connect to the outside world. Zone Alarm is the king of this, its annoying at first because you have to teach it what to let out and what not to. And the fact that rules are per application makes it very powerfull.
3. Anti-Mallware are the following. A must have.
a. Anti-Virus.
b. Anti-Spyware. See above link for a link to a site with a comparisson. You will note from the comparisson that no one protects from all. For your ease here is the link
http://spywarewarrior.com/asw-test-guide.htm
c. Anti-Trojanwares..
d. Hijack This.. this is not a protection tool but more a way to find if you have mallware on your system. It takes a snapshots of your system and you post it on the forums were people analyse it to see what your PC ailment is. Given time anyone can learn to analyse these reports.
By the way If you think your machine is running slow, or something just isnt right. Check your Taks Manger to see what process are running. Sear for each process by its name on Google. Ther are many lists out ther describing what each process is, if it is legit or mallware. Note you wont find everything this way but you can get many this way. Then you can searh for instructions on removing it.
Last and most important. Protection is allways better than disinfection later. There is a case of a person inside a Corporate protected environment instlling a PC with there corporate Windows image, and being inffected during the installation. Basicaly a brand new Windows install should not be connected to the Internet before it has protection. Like the email example i gave above other Worms or bouncing arround the internet still even very old worms. Why becuase they are bouncing from unproteced machine to unprotected machine. Dont be the next PC to give more life to a Worm...
Regards