First and foremost, because there are so many inexpensive web hosting companies out there now, all competing for your business, that you'd get far less headaches and far more reward for your investment than if you try to do it yourself.
Are you technologically savvy? Do you understand what it takes to secure a server? Do you have access to a broadband connection? Are you willing and able to devote the amount of time it'll take to solve the inevitable glitches that come your way one after another?
To host your own server you will need: a dedicated computer (that means it must be used solely as a server and nothing else) with the capacity to handle the number of server requests that (you hope) will come in, a Network Interface Card (NIC) and a broadband connection with a high upload rate, Linux or another comparable O, and an internet service provider (ISP) that will support web traffic.
If this sounds like it's trying to scare you, then you're following completely. With all the inexpensive web hosting options out there, you need a darn good reason to want to do it yourself. Disappointment with one (or even a slew of) bad web hosts is not a good enough reason not to seek out other inexpensive web hosting companies from the multitudes.
If your site is promotional in any way - whether you're selling a product, a service, yourself - an amateurish presentation fraught with technical glitches and poor layout could cost you your business. The average web-surfer has a 20-second attention span, and if they encounter one problem accessing your site, they are unlikely to return.
With minimal research, you can really take advantage of the fierce competitiveness in the inexpensive web hosting industry and find a service that offers mouth-watering promotions, and innovative features unique to your needs. More and more these companies are specializing, and you can find inexpensive web hosting companies catered to your specific operation.
Most likely, if you're considering running your own server it's because your website generates a ton of traffic on more than one website or application. Fortunately, running your own server is not your only option. If you truly believe your capacity is going to be through the roof (high aspirations?) you can find many inexpensive web hosting providers that, for a fee of course, will designate you a dedicated server. This server will be yours and yours alone: you'll share bandwidth, memory, and storage space with no one. And the performance of your site will not be affected by the traffic and usage patterns of any other customer.
With a dedicated server you will have your own IP address and root (admin) access. You have full control over server usage and software installation. Dedicated servers allow you an unlimited number of email accounts and databases and the speed is inordinately faster.
These packages, offered by many of your most common and familiar inexpensive web hosting companies, will often be divided into "managed" and "unmanaged". In an unmanaged dedicated server, you are the administrator. If you like the control, have the time and skills, but just don't have the hardware or connectivity, this may be the perfect option for you. Most folks, too tied up with the day to day of their online business, will prefer the managed option, similar to any other inexpensive web hosting package, simply with a dedicated server.
Consider inexpensive web hosting as a viable alternative to running your own server and chances are you will sleep better at night.