Not sure if I understood your original post, but using new addresses does not automatically make you safe and anonymous. If you have 10 btc and get it from coinbase, they probably have records. Even if you send it to a few different addresses, and have those addresses send it off to more addresses, it's still relatively easy to write a script to group them together when you spend any one of them. If you're paranoid about that, better find a coin mixer, mix your coins after acquiring them, and then transfer them to a multitude of HD wallets.
Yes, when I wrote my original post I did not know that. Can you recommend a coin mixer? If so please let me know. I will probably pick the 'most popular one' and take my chances with the minimum number of coins they let you wash at any one time.
You say: "If you're paranoid about that, better find a coin mixer, mix your coins after acquiring them, and then transfer them to a multitude of HD wallets". Why transfer the mixed coins to a multitude of HD wallets? Hard drive wallets? Is this for security (as in Armory "offline" wallets that live on your hard drive but are not connected to the internet)? Or in case one wallet is stolen or compromised, you won't lose all your money? This goes to security, not anonymity, right?
TonyT
Even a Coin mixer wouldn't really guarantee anonymity. Incase you get into a legal issue, then the coin mixer will have to give up details on thee address from which funds are generated and to which they land into.