I am just looking for a very basic payment solution for my new business. On my website I provide an interface for the user to make the pre-designated payment, and my backend server can be notified of the payment and the user account is immediately activated.
Does Paypal provide such an API? Does everybody have access to such APIs, or there is an approval process?
Would appreciate if someone can point me to a page to start.
Yes, you could do this with pretty much any feature PayPal offers.
Depending on the needs of your business and your application one may be better suited for you than another.
In any case you could utilize Instant Payment Notification (IPN) to get real-time data POSTed to a listener script on your server. Within this you can update your own database, hit third party web services, send out email notifications, etc.