I think Omeka Classic is a great platform for a targeted digital archive (I’m not sure of the consensus, but I think of Omeka S as a better use case only for large institutions with specific institutional needs). There’s a good thread on this forum discussing the differences.
If you’re using one of the default themes, the Contribution plugin is pretty much plug and play. If you’re using a custom theme and/or really want to control the small details, you can create your own modified templates for things like logging in, account management, etc., but that’s pretty straight-forward (be sure to copy the existing templates into your theme directory rather than editing directly).
The plugin templates are as easy to alter/replace as the theme templates if you have some experience with PHP, HTML, CSS, and JavaScript. The Omeka API is well-documented and pretty easy to learn.
You can calculate estimated S3 costs at calculator.s3.amazonaws.com. I’ve configured S3 sites but am less familiar with the pricing side. I think it depends on usage, which makes it difficult to assess if you’re not sure how much traffic you’ll have.