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I would say that the less expensive option would be to use Coinbase. When I say coinbase, I actually mean they trading platform called Gdax, but you just need one account, since you will be using the same coinbase credentials to login into gdax.
You can then deposit in Gdax making a normal bitcoin transaction. You will pay fees here, but only the normal bitcoin fees, that are actually much lower now. Once you do this, you will need to exchange your BTC to Ether, using their platform. The "trick" here, to avoid any more fees, is to place an order at a price that is not the market price (they call this being a maker). This way you will not pay trading fees. It will probably take some time, so you can get your price, but since the market is very volatile, you should be ok.
Now that you have ether, and remember that at this time, you paid BTC normal fees and nothing else. You can now withdraw ether to any address you like, and Gdax doesn't charge fees for withdrawals. So with this option, you will change BTC to Ether, by only paying normal BTC fees.