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The scalability of an application increases with as you go down the hosting options above.
- Your own hardware: Not very scalable. You would need to upgrade the hardware or purchase new / additional servers.
- Dedicated server: can upgrade your plan to a more powerful server or subscribe to more servers however the application would have to be migrated to the new server.
- VPS: you can allocate more resources to the existing server instance without having to migrate however you are constrained as to how much resource you can allocate.
- Cloud Server: are highly scalable, existing instances can be given more resource or new instances can me started and stopped on demand to handle load.
Security
There is not much difference between the solutions in regard to access to the data on the server. The biggest security risk is being hacked which is just as likely with all the solutions.
Management and Monitoring
Most of the hosting providers can provide some level of management and or monitoring however they only take responsibility for the hardware and possible operating system. The bigger issue is monitoring and managing the your application which is your responsibility. It is important to factor in a budget to manage the server / application.
Conclusion
All the options would be suitable however I would recommend against the VPS option. The dedicated server options (either own hardware or leased) would require us to subscribe to a plan that would handle the expected load for the next 2-3 years. Using a Cloud server means that your can allocate enough resources to handle the initial load during your minimal product phase and which acquiring users to keep the hosting costs down and then scale up the hosting plan as needed.