Welcome to TeamViewer!
The TeamViewer Account (aka Computers & contacts list) is saved in the cloud and you can created it on any computer and reach it later from any computer. So you do not have to worry to have it set up on the wrong computer.
You can easily add all your remote devices to your TeamViewer account by clicking on the icon with the person and the + on it:
You will need to add the TeamViewer ID of the remote device to save it. You can save a permanent password as well for unattended access. Each computer has a unique TeamViewer ID which does not change and this makes it so easy to connect to all your devices easily via your TeamViewer account.
I added a few links to the reply which will help you in getting started. Our Knowledge Base has a lot of helpful articles. Please feel free to browse around and in case of any questions, just post your questions in our community again :-)