How to setup domain log in on a network.

I want to setup a domain log in on my own office network with ten computers.
I want to remotely control or access each of those computers.
Do I need to turn off the Antivirus software to remotely access the computer?
I'd like to know also what is the best operating system I can use.
Can I use different Operating System on each computer?
Do I need to use a specific software or hardware to setup domain log in?
Can I access those computers at different locations, like outside the office?
And lastly, do I need high speed Internet do that?
