So, you have to decided to get your own dedicated server. You certainly have a plethora of options to consider: hardware, operating system, development platform, applications, and more. One of the crucial early decisions you must make is to decide where you want your server to be housed.
If you are running a business, a logical choice may be a data closet within your office. For larger businesses, they may even have their own data centers. For a home business, you might choose your basement or a closet in your house.
With those locations, however, it is you or your IT staff (assuming you have one) who must maintain the server and fix anything that goes wrong. Upgrades, both hardware and software, will be completely up to you. You will also be responsible for ensuring you have sufficient bandwidth to handle Internet traffic. The days of using a home Internet connection for web hosting may be over, since major ISPs are instituting bandwidth caps. For good quality and reliability, you will need a dedicated business line anyway.
The alternative is to pay a web hosting company to host your dedicated server. Many hosts will lease servers to clients, either as unmanaged or managed systems. Even the unmanaged systems are usually fully functional and only require some initial setup, which you can perform via SSH or a remote control panel. The benefit of this method is that major IT issues, even for unmanaged servers, are usually covered by the hosting company. You also do not have to worry about the expensive dedicated Internet line or any of the power requirements of hosting your own data closet or data center.
Ultimately, the choice depends upon your means, resources, your budget, and your preferences. Once you make this decision, you can always change later, but it will involve a lot of work to transfer data and setup a new server. Therefore, you should choose wisely.