I would like to ask if you really need ARD, or just basic Screen Sharing?
Apple Remote Desktop is for managing a classroom full of Macs, or a department of Macs.
If you are just going to be connecting to your Mac back at home, then you do not need the paid ARD product.
The Screen Sharing app does a secure authentication. You can then change the Screen Sharing applications preferences to encrypt ALL data.
You can use the iCloud Back-To-My-Mac service to remotely connect back to your home (or office) system.
An alternative would be TeamViewer.com that also uses encrypted connections, and does a very good job of getting through home routers.