The "magic sauce" is to remote into a headless appliance that way your remote session will automatically re-size. If you launch the appliance with VirtualBox locally and then remote into you cannot re-size it.
The alternative is to use VBoxHeadless directly, as follows:
C:\Program Files\Oracle\VirtualBox\VBoxHeadless.exe --startvm "Image Name"
Trouble Shooting
Make sure to turn off 3D video acceleration, it was causing a window to appear on my Windows 7 host, and it interfered with the remote connection.
Had trouble connected to my VM on my LAN, there were multiple Firewall rules with Windows 7. Ended up deleting all of the rules for both Virtual Box and Headless, and when things started again, it allowed access. That fixed the problem.