Hardware
Before we look at the actual PC which will connect to the internet I will outline a few precautions which will be highly beneficial to network security.
1. Use a router, not a modem.
A modem simply directs all internet traffic straight to your PC, which is inherently unsafe for any Operating System.
A router acts as a gateway (or a letterbox if you will). The router is what is directly connected to the internet, not the PC. The router is specifically designed where your PC needs to rely on software to remain safe.
The benefit of the router is that it receives all the ‘Background Internet Radiation’ (Malware/Hacking attempts) and instantly drops it, before it ever sees a desktop PC.
This is a huge advantage for the security of your PC, as it never sees any of this malicious internet traffic. The router acts as a letterbox, as it receives all of the internet packets (letters) drops the traffic you didn’t ask for, and routes on the information that you did ask for to the correct PC.
The router works just as transparent as the modem, with added features, such as allowing multiple computers to access the internet at once, wireless connectivity and maintaining an always on connection.
To put things in perspective, Windows connected directly to the net with a modem, with up to date Antivirus and no firewall, the average time for malware to get onto the PC without the user doing anything, is 13 minutes. A windows PC without any security software, without any windows updates, or a firewall, but connected behind a router will not be compromised without use.
Cost: $130-200, recommendations are ones with a build in ADSL modem, from DLink, Linksys.

Now we have the hardware sorted, malware can only get onto your PC from user invoked actions, i.e. Browsing to a website with unsafe content, opening an email attachment which contains malware, and phishing websites (stealing credit card information).

#1 Get the firefox browser
Firefox is an internet browser (similar to Microsoft Internet Explorer) but built with security in mind. Firefox is written by around 10,000 programmers who donate time, and who have created an excellent browser.
In a nutshell, malware/hackers know well how to exploit Internet Explorer (IE). IE has many known vulnerabilities, with more being discovered all the time. This is the main way malware/viruses infect a PC, that is, through IE. Firefox has proved much harder to break, of which has been solid since creation in 2004. Firefox also manages popup windows well, and even the provision to block advertisements.
Get Firefox from http://getfirefox.com

#2 Keep windows up to date
This is able to be automated by Windows from the Control Panel.
update.microsoft.com

#3 Use a firewall
A firewall is another layer of security which sits underneath all of the applications running off your computer. There are many complicated firewalls with many features, but for home use the inbuilt Windows Firewall is more than sufficient.

#4 Use the internet properly
Many sites on the internet are setup purely to infect your PC, as are many downloads. Sites particularly related to game cracks, myspace, ‘free stuff’, screensavers etc. Also, most downloads with Limewire or other P2P services are commonly infected.
Using firefox is a good defence against many bad sites, but the internet should be used more as a tool, less for simply browsing.

#5 Use antivirus/antispyware
Whilst not required if the above are all used, these products are not a preventative, more-so a patch in case of an outbreak. These applications are not the be all or end all, and never will be. These products help reduce/disable the spread of malware, but they never cure a computer 100%. Nowadays malware is specifically written not to be detected, and if you end up detecting one virus, there may be many more. The only way to remove the malware 100% is to reinstall Windows from a known good source, eg. The Windows install CD.
If you must use an antivirus use NOD32, AVG (Free) or Symantec Corporate. Be sure to avoid the ‘All in one suites’, as they do more harm than good. They all slow down your PC by 20%, but also cause many problems due to locking down the system so much. Do not use Norton, McAfee or any other suite.