I haven't trying deploying the FusionPBX on Docker yet, but my install on Jessie (Debian has gone great so far.
I am going with a $20 Vultr instance next as I plan to run 11 tenants and hundreds of phones off this install. You could probably run it on a smaller install but I don't want to have to worry about resizing discs later, etc. I will be replacing 11 of my $5 vultr instances so overall it drops my host cost from $55 to $20 per month.
http://docs.fusionpbx.com/en/latest/getting_started/quick_install.html# has a great walkthrough of an installation. Use Debian 8 iso for install ($5 Vultr instance for single tenant install should be fine). Judging by github activity this is the most stable setup.
Also, there is a youtube channel https://www.youtube.com/channel/UCN5j2ITmjua1MfjGR8jX9TA that appears to be all Mark, the main developer.
One of the guys active on Github may be coming to give some advice on additional securiting the instal on Vultr (or any cloud instance).
On the security tab it talks about not exposing Mod_xml_rpc to the public. By the default instructions it appears it is exposed, so looking for @DigiDaz to join us on MangoLassi as he has offered to answer questions.
I should mention that the primary developer, Mark Crane, only appears to be monetizing FusionPBX by offering training classes. He is very active on the IRC channel but often redirects advanced questions to his training course. Maybe for those like @scottalanmiller and @JaredBusch who run hosting services that kind of service or support could be useful. I hope we can get enough support going here that a typical FreePBX user could convert to FusionPBX with publicly available info.