Server vs. Desktop
For a small home-server with low-traffic, I'd just buy a regular old PC, or recycle an old laptop. I've got a 5 year old laptop that sits humming on the shelf serving out media and more. Works well, costs next-to-nothing.
You will get more bang for your buck going for a strictly server system because less resources are focused on things like the video and audio sub-systems and there is more focus on the memory, CPU and drive sub-systems. Also, many desktop systems do not support higher level RAID arrays (5, 10). But, in general, for what you're talking about, using desktop hardware is reasonable.
Do not buy server hardware for this. For this use-case, such hardware is absolutely not required.
You buy server hardware where it costs you lots of money to power the machine down, say to change a harddrive.. You don't need redundant power-supplies, hot-swappable drives and RAID for your family website..
Do not use RAID (specifically RAID-1, mirroring) - RAID-1 is used so you can be up-and-running quickly after a drive-failure, not as a backup.. It probably doesn't matter if the site is down for an hour while you restore a backup, but it is a problem if you lose the data!
Instead of RAID, use the second drive to routinely clone the system (every night), or copy important data (the site and file-server contents). It's also a good idea to do an "off-site" backup once a month (either with a second drive, which you send back and forth, or an online service like Mozy)
What you get for extra money on "server" hardware is often partly:
- Hardware support contract with the vendor.
- More "robust" hardware, for example ECC memory.
- "Server only" features in the chipsets and add-on cards that aren't (as often) found in desktop hardware.
- More powerful fans - servers sit in data centers, so noise is less a consideration :-).
I repurpose old systems for my server(s). These were gaming systems in their previous lives, so they're quite capable of some basic server functionality. Hardware failures are an issue because replacing one component in an old system can be quite difficult because the old hardware isn't available anymore.