In short, unless you are the only person with physical access to the server, you are not safe, there is no way you can do this with reasonable effort, a VPS makes no difference.
If you could deploy something like full disc encryption which was only unlocked when you logged in to the system, your provider could still have virtualized the entire server, and not encrypt it anyway, only tell you they have.
Even if you somehow managed to safely encrypt the database, it needs to become readable at the server side at some point, or your server couldn't possibly serve the data.
Either this means that your webserver actually holds the decryption key, making it at most moderately complicated to copy it. You could require the key to be entered every time your http-deamon starts and store it only in RAM, but again, if your host is in a virtual machine you are immediately screwed, and a determined attacker could steal the key from RAM even from physical ram.
I could go on, but the gist is, you can't do what you want without a lot of resources, mainly physical servers in a locked serverrack.