you should make your bitcoin anonymous from the start. which means you should buy it with cash from someone and place it in a new address.
this way it will have no links to you, because buying from any sort of exchange or using credit card would link it to you.
I think this would be a good idea, if a large majority of people had bitcoin and you could find people to sell/buy anywhere in the world... but where I live, there is hardly no one that carries bitcoin or would want to sell them. I've check on localbitcoins website a good amount of times, and still have trouble finding someone in my area that's worth the drive.
Also, it would be nice to have bitcoinATM's to be able to buy with cash... but again, there are none where I live...