Crash course in some of the factors that will make things "Server Grade".
Because a server must have a high uptime, often optimally "5 9's" (99.999%), the hardware must undergo rigorous testing to ensure that it has been produced with a low fault tolerance.
A common factor in all types of manufacturing is a variation in the components. In "server grade" equipment, this is hardware that has been tested and shown to be very, very close to the "perfect" specifications. In CPUs and hard disks, server and consumer grade may be produced on the same assembly line, but the testing determines that some chips (or platters) are simply of a higher quality, thus they are earmarked for server use.
Server motherboards differ from consumer motherboards feature wise in many aspects. Often they have the ability to perform various network boot operations, low level logging of system failures, extensive on-board diagnostic routines, the list goes on.
However, in your target application, use of "server grade" equipment may be overkill. Home servers tend to spend their lives as File Servers, so processor and RAM are lesser concerns. Most consumer grade dual-core processors will be more than adequate for your use.
When shopping for hardware, here are the important things to consider:
Case - Buy a solid case with good airflow. It may be tempting to buy a small case for aesthetic purposes, resist this urge. Instead buy a medium to full size ATX with space for large (120mm) fans. Large fans provide greater airflow and can typically run a lower RPMs, making them quieter.
It is also recommended that you purchase some black open cell foam filters, you can usually buy these at the local hardware store in large sheets, cut to size. Finally, make sure your case will hold all of your devices with some room for air and spare.
PSU (Power Supply) - Don't skimp, but don't go crazy either. You won't need dual hot-swap, but don't get the $15 special either. Pick an adequate power supply from a reputable manufacturer.
RAM - Do not skimp in this department. You won't need a lot (two gigabytes is likely to be the upper limit), but you will want a very high quality. Arguably, good RAM is the most crucial element in creating a crash-less server. Gaming RAM tends to be of a higher quality, check companies such as OCZ and Corsair.
CPU - As previously mentioned, most consumer grade dual cores are plenty. Something in the 2.0ghz range should be sufficient.
Motherboard - Consider what you intend to do with your home server. Less is more. If you are stuffing this in a closet, you likely won't need on-board sound, but you will want an integrated video device. If it's connected to a video output, opt for a "headless" motherboard and purchase a decent media center video display, opt for 5.1 (or greater) onboard sound. Additionally, anything you aren't using should be disabled in BIOS. There are some with integrated RAID controllers, but my own experience suggests either disabling this feature or purchasing one without it.
Hard disks - How many people will be using this at any given time? If the answer is more than two (or two heavy users), opt for high RPM, high cache. If it's less than two (or light use), go with a slower (and cheaper drive), but spend the surplus on additional drives. Capacity is a key factor in a home server. Look at the current amount of media you need to place on your server (let's say 200gb). Planning for the future, triple this (600gb). Now add redundancy, 1200gb (1.2tb), and add one or two hot spares. Additionally, round up in drive size. So in my hypothetical, you would want to purchase 7 or 8 250gb drives. If you purchase two "extra" drives, connect one internally, create hot spare (see below), then disconnect, but *leave it mounted*. Keep the last drive sealed and in a safe environment.
RAID - Purchase a RAID controller card. Many people may argue this point, but after doing this sort of thing for quite a while, I feel this is important. With a RAID controller card and the correct drive set up, your home system should have strong data retention, high speed and excellent availability. When you set up your drive array, using my example above, I would recommend a RAID level 10 array. This will give you great speed with full redundancy. Using the RAID controller utility, create a hot-spare with your extra drive.
I hope this helps.