A remote tool like teamviewer...how do we go about doing it

Hi guys

I would need some advice, I would have to do a project like teamviewer. How do I go about doing it, for now, I have set my eyes on getting a VPS with VPN and a webserver functionality. I would need to create an admin portal as well - a web based where users can add in PC's that they would need to remote in to. Of course, these PC's have to be in the same network. I would need to do an rdp connection and a share screen connection as well.

What is the best approach in doing so, I know..using teamviewer is the best..but we just want to try out something on our own. Appreciate all feedbacks and advices.

Is VPS the right way to go or is there any other better mechanism for this.