The problem I have encountered is the fact that setting it up (anonymous browsing, that is) is far from being a simple and straightforward process.
Not only is not not 'simple and straightforward', it's completely impossible. There is no way you can completely shield yourself from releasing some information since there's always a paper trail (an electronic one, at least).
Even if you use a proxy server (which will mask your IP address from the site you visit), there's nothing to say that the proxy doesn't log the access and therefore you can be traced via the proxy logs.
I also tried the suggestion of using a public proxy. After locating several from a list recommended from one of your links I tried setting them up in the networks preference settings but they simply wouldn't work.
By their very nature, many public proxies are transient - they come and go based on a number of factors including the incentive of the proxy operator to handle traffic (he's going to bear the bandwidth cost, of course), legal matters, and the proxy trying to make itself harder to find by moving frequently.
The process isn't easy and considering that privacy is a serious issue these days I am surprised a simple solution doesn't already exists for Mac users.
I'm confused as to why you think using a proxy in any way improves your privacy or security online. If anything, using an unknown proxy opens you up to all kinds of real issues that are only theoretically a problem if you access the site directly.
You need to bear in mind that anything you download could easily be logged and intercepted by the proxy operator - something especially worth considering should you visit your bank's internet portal, for example. You really are giving the proxy operator ALL your keys to your online world yet you don't know who she/he is.
So when it comes to using an unknown proxy you have to ask yourself whether you trust the person who runs it (whom you don't know) more or less than you trust the sites(s) you're accessing.