Remote Access Across the Internet from One MS Windows Machine to Another

MY SYSTEM
(1) Desktop running Windows 7 Pro
(2) Laptop running Windows 8.1, only 20GB hard drive.

BACKGROUND
On machine (1), I want to install a Virtual Machine that runs Linux.
On that Linux virtual machine I will be installing ROS and running simulations in Gazebo.

I want to install software on both machines so that machine (2), the laptop, can fully control machine (1).
The two machines may not always be on the same WiFi network. The laptop will at times need to access the desktop machine over the internet.
I need to make sure the connection is secure and that no one else can access either machine without my authorization.
I am using this for personal use, non-commercial.

QUESTION
Please recommend software that runs over the internet that will allow me to fully control the desktop machine (1) from the laptop machine (2).
Is there any free software that I can use?
Will Teamviewer allow this?