Help with Custom Forms and Tables

I’d like to create a form that would allow users to add their contact data to the database and sign up for “events” that would be described by a separate table, created by an admin. The contacts and events tables would be linked through a primary/foreign key relationship.

Are there plugins or frameworks you would recommend that support this functionality?

If I decide I need to code this myself, which WP modules do I need to look at in order to add my custom code?

Suggestions to get me started with either of these approaches are greatly appreciated.

Thanks.