Like you said Elastic Load Balancing offers three types of load balancers. Namely Application Load Balancer, Network Load Balancer & Classic Load Balancer. Now as to which one will suit your application, the info below should make it clear.
If you need flexible application management and TLS termination then we recommend you to use Application Load Balancer. If extreme performance and static IP is needed for your application then we recommend you to use Network Load Balancer. If your application is built within the EC2 Classic network then you should use Classic Load Balancer.