There are many exchanges and platforms which offer the possibility to buy cryptocurrencies. The most of them charge ridiculous high fees and as far as I know all of them require an identification process. I tested a lot of them. It was nerve-wracking experience and therefor I wanted to share my findings with you.
The easiest and cheapest way I found is to buy on gdax
https://www.gdax.com/
Gdax is an exchange, from the popular and renowned company coinbase, where you can trade directly with fiat. An advantage there is that you don't have to pay a fee to withdraw your cryptocurrency. It's really convenient especially when the bitcoin network is overloaded and the fees are insanely high. The only downside is the required wire transfer from your bank account which means you have to wait a few days until your account is credited.
If you are in a hurry you can also use their main site and buy your coins with a credit card. But be careful, they will charge you a few percent and you will get an unfavorable exchange rate.
An alternative to gdax would be kraken.com where you also have good conditions, but their website is unbelievable slow and buggy.
Just in case you don't have an account on coinbase / gdax, I would really appreciate when you use my affiliate link https://www.coinbase.com/join/59afd2db624cdd02bf1c866c