Hey Peter, welcome to the forum! 
My first recommendation would actually be to take a little search in the forum. Don’t worry, this is not the usual “do a search” that you get in forums, but chances are high, that other users had done this transistion already and there could be some useful ideas and experiences in these threads. So yes, in a case like this, I really do recommend to give the search a shot - in addition to you asking here. 
A recomendation for hardware is always difficult, as there are many factors to take into account, especially your personal preferences.
But as Tom said, the GREEN is a fine device, that’ll fit your description. If you want a little more DIY, a Pi is a nice device. And if you want to go crazy from the beginning, go with your own little server, like a mini-PC and eg. Proxmox as virtualization.
For the devices you have, a GREEN is suitable and will not lap in performance. And you have an all in one device.
If you really dig deep into Home Assistant and home automation, you’ll likely buy something “bigger&better” in the future. If you’re staying with your setup, and not get crazy, you’re good to go for a longer time with the GREEN.
As you asked about your transition. If you like Home Assistant, here are two links that might be interesting for you:
And especially this one (that is listed in the cookbook as well):