@Kainuk, I've implemented three instances of CiviCRM / WordPress / LAMP on AWS, and am in the process of converting two of them to public production, the third has been running private production for about 14 months now. All are implemented on t2.micro instances on Ubuntu (14.04.3 - LTS). Each has a very small audience (regional < 1,000 expected public users and < 10 backend / database users per instance) and is purpose built for a specific not-for-profit organization and its audience. @naomi says "no specific settings are needed for CiviCRM;" I agree. That said, it can be challenging, because there is not a large community in this space. The support you get is the general support available to CiviCRM and WordPress, not so much directly for AWS. So far, that has not been a major issue.
I am using these AWS Services: EC2 - compute / memory (EBS), Networking - VPC and Route53 - DNS, Cloudwatch - Basic monitoring, and IAM - User management. The first year of use is basically free, beyond that, for my groups, using reserved t2.micro instances on a 3 year basis, costs run ~USD 100.00 / year, each. With current low loading, performance has been entirely satisfactory.
I have put up a general how-to article on the CiviCRM wiki, which provides more details. I'm eager to continue the conversation and wish you success in your efforts.