I think you should buy localbitcoins account or paxful account because you can't buy bitcoin with new account
Local bitcoins seems ideal to me because you can remain anonymous and even meet in person if you agree and have your bitcoins transferred without any form of identification. How simple, so I will recommend that any day.
If OP doesn't want to reveal his ID documents to anyone then i really doubt that it is likely he wants to be meeting someone in person either. Localbitcoins is a good place to go to if you just want a clean, safe and convenient deal with someone, but in my opinion choosing the right payment method is just as important as choosing the right exchange.
for example if you use paypal, then your identity is out there. Same thing with bank transfers and credit cards, even if you're trading on localbitcoins. So stick to cash deposits, cash in mail, etc. if you want to remain 100% anonymous.
Runners up for anonymous exchange would be paxful, a lot more gift card traders there but you'll get worse off rates overall for the convenience. But paxful is definitely more private than localbitcoins, for LBC you need a mobile phone verification and some offers are limited to ID verified only.