The right way to do it is to empty and then write-protect each file or directory containing your browser's data (this is far easier to accomplish with Mozilla and Firefox than with IE, by the way, because the 'zilla products don't stash browser traces in the Windows Registry or scatter them about the disk; all of the relevant files and directories are in the user's Moz/FF main directory). Follow that with a proper wipe of your disk's free space, and you'll be in good shape.
Of course, if you do purge and write protect your browser's various history/cache traces, you must not log in routinely as the administrator or root, because such high user privileges will override write protection. It's best first to do the data purging and write protecting for each user as root or the admin, and then to run your browser from a user account thereafter. This way, there simply will be no browser data written to disk, which is the only way to be truly secure and private.
If you're privacy conscious, but concerned about browser slowdown when the cache is unavailable, here are two tips that will help:
Second, you should know that much of what slows a web page loading is the simple job of drawing it on your screen. So if you've been giving thought to buying a better graphics card, here's another reason to get it. A good graphics card will improve your surfing speed noticeably if your system is a little underpowered.
Back to the privacy issue. Now, in addition to having no option to block third party images, as Mozilla has, Firefox has no option to prevent link prefetching, again, as Mozilla has. Now, perhaps Firefox doesn't do prefetching, but without an option addressing it, one has no idea. Prefetching uses a browser's idle time to cache content that one might be interested in. When you elect to follow a link, the content is in your cache already and loads faster. It's not the best thing for data hygiene, although I should note that if you've emptied and write-protected the cache, it's less of an issue, because there is no place for prefetched content to go except memory (which, under some conditions, could be written to your swap file). In any event, if you're privacy conscious, it's always best for you to decide what content your browser should access, and not let it be done automatically.
This is not to say that Mozilla is flawless. One particularly galling bit of behaviour is the way Mozilla Mail can keep your cookies active after you've closed the browser. If you've set all cookies to expire at the end of the browser session, you mustn't forget that Mozilla Mail has to be closed too, or the session might not really be over. And if you've got Mozilla Mail minimised to a little tray craplet, you might well forget that it's running. You could have a session with your bank, or from a very private web mail account, remain active, and the next person using the browser might be confronted with a lot more information than you'd ever want them to have.
Firefox doesn't have this problem because it's a stand-alone application, so there's less overlap between Firefox and the Thunderbird email client than there is between Mozilla and Mozilla Mail. However, Mozilla users can avoid the problem simply by using Thunderbird or another client in place of Mozilla Mail (personally, I use Linux with the Mozilla browser and with Kmail, which I find immensely more secure and configurable than either Mozilla Mail or Thunderbird).
In spite of this little cookie irritant, I still consider Mozilla slightly more secure than Firefox, although I will allow that I used to regard Firefox as absolutely unsuitable from a security and privacy perspective. It's come a long way, and is now only marginally inferior to Mozilla, which, as just noted, is hardly perfect. Nevertheless, Mozilla remains potentially the most secure browser available - assuming you take the time to configure it well. Firefox is a close second, and I would no longer advise anyone to avoid it.
I would like to see an option to block third party images and an option to prevent prefetching, and I'd like to see a little disclaimer along with the option to clear personal data, since it's hardly secure, although it is certainly better than nothing. And Firefox really has come along nicely in terms of privacy and security features. I sense that it won't be long before I'll be recommending Firefox in favour of Mozilla. Not today, certainly, but soon, very soon. ®
NOTE: Do not, under any circumstances, inform me of what I already know can be done with the about:config menu. Most people are not power users. These settings need to be available in the main, GUI configuration menu. --tcg