remember, all the solutions mentioned so far are self-managed. So you may find yourself spending a decent amount of time hardening and maintaining the servers regardless of whether you get a dedicated server or cloud VPS.
You may want to consider a managed VPS where the patching and security updates are done for you by people who do this for a living. It depends, I guess, on the nature of the apps you host and how much a data breach would impact you.
I have heard (but not used personally) SquidX is good for managed VPS. I am sure there are others. There is a section on WebHostingTalk on fully managed servers if that is the approach you take.
