Amazon Route 53 is the official web service to host your dns zone into AWS; it's a very reliable dns service, it relies to the Amazon Global Infrastructure. Also you cannot choose the Region where host your zone because dns service is global by definition.
Advantages of Amazon dns service
strictly with all other AWS web services like: S3, Cloudfront, EC2; for example you can link your external resources
- it relies on Amazon Global Infrastructure
- health checks for certain Resource Records; for example you can implement easily failover strategies for a remote disaster recovery (DR) site.
- mitigate any dns DDOS attacks; theoretical Route53 can mitigate attacks based over 70Gbit/s!!!
- map on-premise computing resources with external dns service
- low latency resolutions based to nearest resolver node
Keep in mind that dns service is a functional key part of to build high resilient and scalable infrastructures; you can compose perfectly your computing resources, but if dns service doesn't work your scalability strategies will fail.
Buy your domain
You can buy externally with some other registrar like BlueHost, Godaddy, OVH or whatever; in this case you must specify the authoritative dns given from Route53 to take advantage of all features. To buy a new domain login into Management Console and to go Route53 management page:
Then click to the big blue button "Register Domain" or "Transfer Domain" and follow all the steps. Remember that the registration or transfer costs will be charged immediately to your Credit Card; also please check your funds.