you can use a VPS and for example one FTP Backup or on other vps for backups,for security and prevent your data from access you can use managed vps if haven't more information about managing your server/s.
there is some other choices which depend on your budget and level of your data sensation.
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Take necessary actions like data encryption, possibly multiple levels of authorization for the data, etc. VPS = you will have more control on your data / installations and will be more secure compared to a shared environment ( I have heard HostGator uses some File System isolation for shared hosts; but not sure how effective it is and it is better if we can extra precaution from our end ). And your next consideration should be your budget Even with VPs, consider storing your data in a secure manner always.
There are several hosts that using CloudLinux's CageFS. I'm not sure if that would be enough safety. Like others have said, a VPS would offer greater control. There's a lot more you could do with it.
But, I think it's also important to note, you need to make sure that you keep the VPS in line, or have management by a good company like Rack911 to keep it ironclad. If you get a semi managed VPS, and don't keep it under control, it may be worse than a good shared account.
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Definately will be much better!
Not sure if HG is the best platform for it however. You would need a reliable VPS. Best if you pick one from the forum here who can help you with setting it up and providing additional security.