There's one thing regarding setting up VNC software I forgot to mention. It was important for my situation, which may not be common. There was another thread recently about remote desktop solutions, but that thread was labeled Mac, this one Chromebook, so either-or. The issue is machine-independent.
I happen to have a separate DSL modem / router-wireless configuration. I went to DSL because my cable provider's (Comcast) ability to keep the connection alive was just unacceptable/awful. DSL has been far more reliable, at least where I live.
I didn't notice this until I tried opening ports like you have to for VNC software to work properly. Most other typical activities (web browsing/email, etc) just worked with the units in their default mode.
But as I understand it, the problem arose as to who (between the DSL modem and router) "owned" the external IP address visible to the world, the one assigned by your ISP. All the stuff "behind" has its own, local IP address following "private" internet standards.
Without the change, the router/firewall was given a private address (192.168.x.x, I think) and port forwarding did not apply to traffic trying to enter. The DSL modem, as far as I could tell (it's manufactured by Westell, sold by AT&T), didn't support that kind of port forwarding. I gather most DSL setups integrate the modem and router, so maybe it's not an issue but it was for me.
The solution was to set the modem into "bridged mode" (you do that through its management web interface, and it complains before it lets you do it), after which the modem just says "OK, I'm out of this, I just pass things through" and then the router gets ownership of the external IP address and will forward ports as directed. It took some work to find this out but everything worked as expected afterwards.