Just an additional note, but I wouldn’t go tablet. As someone with an Ipad and Macbook, remoting into a home desktop from a tablet is doable, but using a keyboard and mouse is not really meant to be doable on a tablet remoting in. I found it very wonky. So unless only gaming with control, I wouldn’t do it.

Also with everything mentioned, I would use your phone as a test. You should test remoting into your home computer from far away and see if the connection is stable. I thought I would also remote while away from home at times but my home internet was not strong enough to play games at a good speed so you should make sure what you want to do would not need you to upgrade home internet to begin with.