If a client is extending the Project for a longer time, which hosting is best? Managed VPS Hosting / Cloud Hosting / Unmanaged VPS Hosting? or any other?
Depends entirely on the needs of the client, and also the competence - if the client have no clue, an unmanaged VPS would not be a good fit, for instance. If the client is creating a small platform/web-site, cloud hosting would be overkill, and so on and so forth. It's impossible to say, based on the information you're providing.
Yes I agree with you to manage a project for long time, you have to depend on the needs of the client.
It depends on client. What he needs. If he has knowledge about linux and can manage himself them go with low cost unmanaged vps.
Managed VPS Hosting or Cloud Hosting would be ideal because you wont have to worry about the server management part.
Managed VPS Hosting is the best option. A provider that offers managed vps, will take almot all care of your vps as their own server.. Things that will be included is such as proactive OS updates, application updates, security patches, proactive audits, fine tunning of services, installing applications, monitoring services on vps etc.
Among the options you have given, you should go for Cloud Hosting because it is easily scalable. When your website grows, you can increase the server resources instantly without any downtime.
The length of time isn't an issue unless you're worried that some flash in the pan cloud host won't be around long to us. Ultimately this will come down to the resources you need. VPS is pricier than shared hosting, but you're not sharing and that's great. In terms of that, I would recommend a managed VPS host like WiredTree, who has a great reputation for service and support.