Don't have much experience with the other options you mentioned except for Teamviewer. Get the "Teamviewer for Windows." It's pretty straight forward because it will ask you upon installation if you want the computer to serve as "a computer you connect to" or as "a computer you use to connect to your other computers." No need for any technical configurations or anything. Almost as simple as plug and play.
So you use the same App "Teamviewer for Windows" for both your working terminal as well as your rig? Are you able to set an authenticating detail on your rig or do you have to re-run the Teamviewer Software each time you re-connects.
From Teamviewer: TeamViewer Host is used for 24/7 access to remote computers, which makes it an ideal solution for uses such as remote monitoring, server maintenance, or connecting to a PC or Mac in the office or at home.
It seems Teamviewer Host is for long term remote access solutions. Confused too.