These recommendations are what I typically either install or suggest to anyone who is less than proficient with computers, and also use myself.
Browser: Mozilla Firefox
Really the main reason I suggest this browser is the Adblock Plus addon. Now I know that websites need ads in order to be profitable, which is why they exist in the first place, but a great deal of these ads are very misleading. In many cases they are setup to look like a download button ( CNET is a prime offender ) on pages where users are searching for legitimate software ( such as free anti virus ) and cause the less than skilled to download adware. Until ad companies phase out these misleading ads, this will remain my preferred settings.
In one case I suggested a free anti virus to a friend, and he ended up downloading some horrible malware instead because he could not recognize the difference between an ad and the actual download location. Who got the Blame? Me of course.
Another addon I highly recommend is WOT or Web of Trust. This allows a user to rate any website based upon how trustworthy it is. There are many similar tools available, but this particular one is the most highly used. Keep in mind that many websites are unfairly ranked poorly due to advertising techniques, but that is another issue. In my personal opinion, the pros in this case greatly outweigh the cons.
AntiVirus: Avast or AVG
Either of these will be effective, and there is very little difference between the two. It is imperative to have an antivirus program installed, and the free ones provide almost as much protection as the paid versions.
Paid versions typically do more to monitor your network security more than anything else, and is really only essential for advanced users. In a rural area such as where I live, you would have to be so close to my house ( and trespassing ) to hack my network that you are likely to be shot.
Now these programs are more suited to repairing damage already done from NOT using my recommendations, but will end up being important at one time or another.
Spywarebot: Search and Destroy
You can save a great deal of money using these programs by not having to take your computer to a grossly overpriced repair shop. Call any computer shop and describe just about any problem. The very first thing they will almost always say is "Sounds like a virus". This is why it is much better to be proactive, and these programs are essential.
As always, be vigilant and read user reviews from third party sites before installing anything. And NEVER click on a link from your email in order to log into ebay/google/paypal/any site at all.