OT but what I really want is a service where I just click a button and they configure the server for me with automated security updates.
Not really.
What Terraform does is to allow you to put all your configuration in (versioned) code. So you can have all your existing configuration, and then change the relevant definitions to Digital Ocean or Linode and make the commit 'Move to DO/Linode'.
Exactly how its configured - security or otherwise - is still up to you though.
> OT but what I really want is a service where I just click a button and they configure the server for me with automated security updates.
Why are you moving from Heroku to Digital Ocean then? Heroku is much closer to, if not exactly that.
It basically comes down to the daily cycling which I have no control over and the low memory on the hobby dynos. My game is constantly reaching the limit and without rebuilding the whole architecture it leaves me with either upgrading to a much more expensive dyno or migrating away.
I also miss just being able to ssh into my machine and do stuff.
I'd first ask what makes you want to move out of Heroku, especially if you have no sysadmin experience at all.
Re OT: you should really check out https://www.engineyard.com/, which provides a layer of services on top of AWS. You can handle a Rails or Node application with little experience and have security updates (Disclaimer: I'm a happy customer, but again I use many different providers so I don't think I'm too biased).
See my other comment for reasons why I want to move away from Heroku. I can expand on the cycling bit though:
I keep my game's state in memory all the time and really just want to write to the database once in a while. The random cycling prevents this since it just terminates the app without any warning so any state is lost.
This is all anecdotal but at work we recently switched from marketing sites/blogs on internal infrastructure to farming them out to DO. The biggest concern with the person who manages our fleet is the security implications of handling multiple machines outside our network. In just a very minimal amount of Google fu I found a plethora of management services that do the work you're talking about on your VPS infrastructure. Some specialize in just DO but a large number are relatively cloud agnostic.
We have also just recently invested in using Laravel Forge for provisioning and it's relatively trivial to write a script that will run 'sudo apt-get update' but proper security usually requires a bit more than that. Package upgrades to major versions can sometimes cause quite a bit of havok. Having a service or team of individuals that can keep this brain power to handle your case properly is often more than worth the price to someone like me. Finding the right one is its own chore but from my limited search there's quite a lot out there to cover just how hands off you want to be.