Let visitors sign up to my courses?

I want to let users sign up to my courses in a way that feels professional to the visitor and is easy to administer to me.

The ideal solution I can think of is:

-having a button/link next to each course

-after clicking on a button/link, the visitor is taken to a new page (or an area appears). A drop-down has a value pre-selected depending on which course the visitor selected. There are other text fields that ask the user to enter his name and things like that. There is also a send button.

-When the user clicks the send button he get’s a message that “Thank you for signing up” and I get some kind of message telling me who signed up to what.

What is a good way to do this in WordPress? Is there a plugin for this perhaps?