Kali is certainly a good pen testing OS, (it's at least one tool used by training companies for this sort of thing.)
As a question, what are your plans for pen testing?
Are you planning to just test your network against "known" exploits?
Are you planning to use "known" exploits to "hack" "your own" network to see how far these exploits actually get you?
Are you planing to write/develop your own exploits?
and I guess what OS do you normally use/are comfortable with?
(if you're a windows only planning to run an exploit checking tool to see what stuff is exploitable on your network, then there are tools like Nessus available for windows, and you won't need to learn a new OS)
to your broader question...
Anonymous web browsing can be achieved perfectly fine with a tor browser (any OS), though by and large, what you need to think about it not so much whether someone can trace your browsing directly to your IP address, more, can someone trace your activities through data that you personally leak. (for example, checking into public mail services, re-using online handles, slipping family details, where you live/work etc.) regional specific dialect/slang...
Really the need for anonymous browsing does depend on what you want to do, and why you may wish to maintain anonymity.
