TeamViewer doesn't remember size and position of its own window for 2 years!
For two years now, there is no way you can get TeamViewer 15 for Windows to remember the size and position of its window. Is it so hard to implement a simple function that works great in other programs? A hundred times a day, you have to stretch the program window to the same desired size and drag it to the same convenient position! In addition, TeamViewer does not remember the monitor on which it was displayed during the last session, which is also inconvenient.
There are some basic defaults that you can set for windows and scaling, though it sounds like these won't be enough for your needs. In the application, in Computers & Contacts, right click on a system or group, click properties, then the advanced button at the bottom left. This will allow you to create some default options every time you connect to that system or systems within that group.
If this does not fit your needs, try adding your request to Ideas and feature requests. Your ideas may be added to a future version.
TeamViewer user since version 6 (2010). We used other remote software programs (TVNC UVNC PCAny) for many years before.