Let’s start with the root server. The biggest advantage here is the price. Root servers are available from 40 $ / month. Another advantage is that it is not subject to any restrictions. A root server is usually pre-configured with Linux and the usual server services. From then, you’re on your own. I.e. you can install and configure whatever you want, but you are also responsible for the stability and security of the server. One should not underestimate the effort in the administration of an Internet server, including some necessary experience.
If anything goes wrong, there is usually a way for the server to put everything back into its original state. This is except when everything updates or is configured. Of course, you can also seek the support of the hosting service provider, which is good, but you can end up paying for the service.

My favorite is the managed server. Here the prices start at around 100 $ / month. With a managed server, the hosting provider takes care of the administration and maintenance of the server. Especially for freelancers, like me, this saves valuable time, time where you can enjoy your beer in the evening, and relax a bit more. The disadvantage of this approach, is that a larger system change with the hosting service providers need to be coordinated, since this is indeed responsible for the security of the system.

The solution for real men is instituting their own hardware. Here you set the server at your office, and then get into the center of the provider. This provides a place for the server network and power cables. The rooms (and racks) in the data centers are air-conditioned and have a secure, uninterrupted power supply. The costs calculated here are mostly high.
Ordinary server chassis have a width of 19″, and a height of one to four rack units. A lower monthly fee is paid for a server with a rack, but it also has less room for drives, fans and Co. Here, I would recommend a server with two rack units. Note that your fans are in good use. The most common problem with servers of only a few units, is the amount of heat, especially when there is a higher load on the processor, and it is operating multiple disks.
There are AMD processors, rather than those from Intel, but it does depend on various circumstances. After some disappointments with SuSE Linux, the current operating system that has the best experience with, is FreeBSD. Generally, however, Linux is also a good choice for an Internet server. I would not suggest it form Windows, though, but is a matter of taste and you have to choose for yourself alone.