Karl, there are more reasons for wanting to keep a low profile on the net than being a criminal or a pervert.
I think the situation is a little different in Europe, but here in the US it's gotten so that almost everyone is a "criminal" --because there are so many thousands of laws and rules within so many government agencies that it is almost certain that every US citizen has violated some law they didn't even know existed without meaning to do anything wrong. All it takes is someone from one of our agencies to decide to investigate and it may turn out you have violated copyright, infringed on a patent, or damaged the environment and must pay a hefty fine or spend some time in prison.
But to answer
mikeschn, I would simply use the Lucid 5.2.8.005 Puppy and install the TOR browser, which is essentially a hacked Firefox. It's already packaged for you in the PPM. Then I would use a site like qrobe.it (a Firefox add on is available, and with SSL, too) for my searches (Privatelee https is the same thing) or even Startpage SSL to search with. While you are at it, check out the list of secure shell add ons by "SSL Toolbar" and see if there's anything there that you would like to add.
And even with all that you will not be totally untraceable, but unless you are in need of serious anonymity, it should be enough.
Also, check out the live distros "Liberte'" and TAILS on Distrowatch. Later, you might be the one to respin the next TORPup...
It's a fascinating subject, but anonymity on the web is easier said than done. If someone is out to get you, all you can do is slow them down. It is very unlikely that you won't get noticed somehow...if only because you have an IP provider.
I play with this stuff in a very non-serious manner; that is, I have fun with it, but don't really use it for anything. My everyday Internet activities are quite transparent, and that's my choice. But not everyone has the same needs --or level of paranoia.