You'll then have to consider your disaster recovery plan. Backing up your data should be relatively straightforward, but what will you do in case of a hardware failure? If you are financially capable of doing so, the best strategy would be to buy two of everything. This will provide you with easily accessible spares in case of a hardware failure.
Now that you've considered the network and server hardware, we need to discuss software. When running your own webserver, you are responsible for the upkeep of your operating systems and all other software you'll be using. The most significant part of this task is the maintenance of security patches. Depending on your server's operating system, this can be a very simple task, or a more involved task. Make sure you know your operating system well since you will be responsible for system security.
Web hosts offer features such as climate controlled server rooms, emergency generators to provide backup power and physically secured rooms to prevent unauthorized personnel getting close to buttons, power cords, switches, etc... Though these features are critical for a company with racks and racks of servers as well as contractually obligated uptime commitments, you probably don't need a physically secure, climate controlled room. Depending on where you're located, power outage risks may be easily mitigated with a couple of medium sized UPSes.