Which storage class would you use for website hosting files?

It depends on how often we accessing the data, availability, durability and performance. S3 Standard is best option for high availability, high durability and performance with frequently accessed data. If unknown or changing data patterns, best alternative is S3 intelligent tiering for automatic tier but slightly more cost.

Which storage class is best for frequently accessed data?

S3 standard offers high durability, availability and performance object storage for frequently accessed data

If cost is more important than availability, which storage class may be used?

S3 One Zone IA is ideal for customers who want a low cost option for infrequently accessed data but do not require availability resilience of S3 standard or S3 standard IA.

What is the benefit of S3 Intelligent-Tiering?

The amazon S3 intelligent tiering storage class is designed to optimize storage costs by automatically move data to the most cost effective access tier when access patterns change. For small monthly object monitoring and automation charge. S3 monitor access patterns and automatically move objects that not have been accessed to lower costs tier.
S3 intelligent tiering delivers automatic storage costs savings in three low latency and high throughout access tiers.
For data that can be stored asynchronously , you can choose to activate automatic archiving capabilities within the S3 intelligent tiering storage class.

What is the difference between public and private buckets?

Objects placed in private bucket can only be accessed using the bucket credentials unless it is shared with others specifically. Objects placed in public bucket are accessible to anyone with the link.