As you can see there are a multitude of different options which all have their pros and cons. I'll try and summarise.
Hosting options
Hosting of you own hardware
You purchase the hardware and pay for the hosting / connection to the internet in a data centre and are responsible for everything.
Dedicated server
With a dedicated server you are leasing the hardware from the provider and paying for the hosting of the server and connection to the internet. The provider is generally responsible for the upkeep of the hardware and replacement of and faulty components (hard drives etc.). We are responsible for everything else, however most provider do provide the service of managing and monitoring the server and making sure all operating system security patches are up to date.
VPS (Virtual Private Server)
A virtual private server is a segregated space and access to the resources of a much larger server. There will generally be many virtual servers on the same machine and the provider will allocate resources according to your subscription. None of the other virtual server have access to each others data however resources are generally over subscribed as not all virtual servers will be running at 100% utilisation. This does mean that occasionally other VPS instances on the same hardware can effect your application.
VPS are becoming less prevalent with the increase of Cloud servers.
Cloud Servers
Cloud Servers are similar to the VPS model however instead of multiple VPS instance on single hardware many individual server are connected together to produce one very large cloud of servers, you are subscribing to a segment on that one large cloud. The advantage over VPS is that the resource are spread across a large number of server which reduces the chance that other applications can effect your application and you can scale up you server much larger then you can with a VPS service.
Scalability
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.