How to get started with program that can search emails and interact with links within them

I would like to make a program that can connect/log in with outlook or gmail via API and follow links that are located within certain emails. The program should then follow the link to an internet page and be able to log in on the page and press a button.

I have only just started to do some research, and no post here gives a complete solution to my problem.

So i thought i would ask for help here, to guide me on my way.

The program need to be able to:

1. Connect to Outlook or Gmail by API.
2. Read specific emails that are are chosen based on the date and time they are recieved.
3. These emails contain links to another website. The program should be able to follow these links to another website.
4. The program should log in on this website.
5. The program should push a button once logged in - this button can be identified via an id in the html.

I have had a basic CS course and have experience with HTML, C# and a little bit of javascript (very little).

I imagine this can be done with a combination of javascript and maybe C#?

If you want to help me to get started i would appreciate it alot. What do i need to research? How would you approach the problem?

Thanks in advance.