It depends on your budget, but if you have a minimal amount of traffic, then I would suggest VPS. But if you have a full-fledged office with good or minimal traffic I would suggest Dedicated Server as it gives more power to your IT department.
Most people would do much better with a virtual private server (VPS) than a dedicated server, particularly if you go with a cloud VPS provider. A cloud VPS offers many of the same advantages like a dedicated server, but at a lower cost and with much more flexibility.
I recommend a dedicated server since it allows a client to tailor the server to their specific needs in terms of CPU, RAM, disc space, and software. Customers who use shared hosting are limited to the programs, software, and operating system that are already installed on the server.
It always depends on your needs and requirement. As you stated its an medium scale organization. I will suggest you to start with an VPS in your initial phase and check its satisfying your needs. If you require more resource then you can always switch to Dedicated server.