If you already have an account on Coinbase, you can buy some BTC, ETH or LTC using GDAX without paying any fees ! You don't have to create a new account because GDAX and Coinbase are sharing the same backend and transfers between your Coinbase wallets and GDAX account are instant and free.
If you want to create a new Coinbase account, use this link to get $10 bonus : https://www.coinbase.com/join/59a911e1692a1d00c0efeb81
Here is the trick : "When you place an order which is not immediately matched by an existing order, that order is placed on the order book. If another customer places an order that matches yours, you are considered the maker and your fee will be 0%."
Here is the video explaining how to place a limit order to avoid fees when buying bitcoin, ethereum or litecoin :
Transferring funds between GDAX and Coinbase : https://support.gdax.com/customer/en/portal/articles/2430129-transferring-funds-between-gdax-and-coinbase