Easiest way would be to get Bitcoin first, and then get Ethereum with your bitcoin.
For this, you pretty much have a range of options. Obviously there is localbitcoins which I'm a big fan of, but there are also fiat exchanges that you can use. Kraken, Bitstamp, etc. In fact they all have ETH listed mostly as well, so you could get your fiat deposited and then get ETH straightaway if you wanted to as well.
For the quickest trade without any verification though, go with localbitcoins. Expect 5-7% above spot price for your fiat though, which is a bummer since otherwise they are the perfect trading platform. Then go exchange that BTC to ETH on shapeshift, expect another 5% above spot price deal so in total you'll be losing out on around 10-15%. Not a great deal, but it's fast, and no verification anywhere.
Localethereum seems to work as well. Haven't tried it myself though.