I've created an app to solve exactly what you described.
With Personal Discount you can automatically generate a unique discount code for every new subscribers. Then you can send the discount code from Mailchimp by setting up an automated welcome email.
As for the pop-up, you can use the one offered by Mailchimp (Manage Audience > Signup forms > Subscriber pop-up) or a 3rd party pop-up app.
Please let me know if you need any help.