After you have purchased a D-link router you can sign up for the Dlink Dynamic DNS service here https://www.dlinkddns.com/login/?next=/
When you sign up they ask for the MAC address of the router (to verify that you own a dlink router). There are other free services as well such as Free Dynamic DNS - Managed DNS - Managed Email - Domain Registration - No-IP but I have not tried them, since I already had a Dlink router.
As far as IP camera is concerned there is so much variety that it is difficult to recommend one. There are a number of factors which affect price, Fixed cam or (PTZ) Pan, tilt, zoom camera, 1080P or VGA, 15FPS or 30FPS, low light performance. The best way to select cam is to check online reviews for IP cameras and choose one that has best features based on your budget.
Port forwarding is configured on the router. When you are trying to access the cam from the Internet, the router firewall will block you due to security reasons. You basically need to configure the router to allow incoming connection on the port that the IP camera is configured to use.
While enabling remote access do keep in mind that network security is paramount. By allowing incoming connections you are opening a backdoor to your home network, so you must protect it with strong passwords. No more 12345 passwords or using the same password for everything. Also, only access your home network from trusted devices and computers that are in your control, not shared computers.
