What is the cheapest way to acquire bitcoins? What is the cheapest and easiest way to acquire bitcoin for a beginner?

I bought bitcoin from an ATM and had to pay 10% premium. I downloaded a mycelium wallet on my iPhone and I noticed that the fees are insane. A minimum fee is currently 12,68$ and if I want to send bigger amounts the fee is around 15%! I think these fees are just pure madness. I am currently looking different online sites but I don't know which one is the best. There are so many out there. 

Could you guys help a beginner to buy some bitcoins?
Those fees are madness. Currently, transactions with a fee of 40sat/byte are being cleared. The problem is that fee estimation is not as easy as it looks. Fortunately, I believe Mycellium has the option to input a custom fee.

Buying at localbitcoins.com is one option, or using an exchange like GDAX. Usually, buying larger volumes is more lucrative than buying lower volumes.