TL:DR
TigerVNC is likely the easiest to setup and use. Remember to run VNC over SSH.
There’s barrier - but that requires you to have a monitor attached to the system
Then there’s TigerVNC - which does not require a monitor but can be used to control any graphical system
Teamviewer is a proprietary solution - where you connect using Teamviewer servers - good for remote support of users running Windows or Mac - not so good if the user needing support is running Linux and not technically minded.
Theres also NoMachine - which I know nothing about.
It is also possible to use xdmcp - this allows for starting a single program - sending only the screen over network - the protocol is unencrypted so it should not be used with untrusted connections - it can be run over ssh - makes it more secure.
That one is new to me - thank you for that tip 
x2x has a long history. It was born in the times when life was hard, window
managers were simple and displays were rectangular. Now it needs an overhaul.