What are the advantages of using AWS nameservers as opposed to servers provided by other registrars?
There are two parts to owning a domain. The registration, and the hosting of the DNS entries. As you are transferring the domain registration, AWS needs to know whose service do you want to use for managing your DNS host names and other settings.
As a sensible default, select option (1) as this will keep everything managed with the current registrar / hosting company and so nothing will break (at this point in time). When your hosting expires with this company, its quite likely they will drop all of your DNS settings as well, in which case you will need to have migrated somewhere else before this point (options 2 and 3)
However, if you are using AWS services you really should be managing the DNS settings in AWS and create a Route 53 hosted zone. This provides better integration with the AWS environment, and allows you to use some of the &quot;AWS aware&quot; aspects of Route53 for your infrastructure.  Assuming that you initially selected option 1, you should then set up a parallel zone in Route53, verify all of the DNS records match (except NS settings for the domain) and then update your Domain registration to use option 2. Changing this setting can take 72 hours to roll across the internet. In my experience, usually 90% of the internet knows in under 6 hours.
Option 3 means you (or someone else) is managing the Domain DNS master server for your domain. There may be situations where this makes sense, but they are rare.