Shoot for reliability and usability.
Intel Pentium E2140 ore E2160 or earlier. The Intel Core 2 Duo range has been highly successful and reliablel, delivering unbeatable performance at a variety of prices. The original Core 2 Duo E6700, E6600, E6400 and E6300 processors have been great.
But the less costly AMD cpu would be every bit as good a choice for a family computer.
Those combined with an excellent motherboard from FoxConn, Intel, Gigabyte, or ABit will make you a hero.
One way to save, is to look for a motherboard cpu combo package from
www.tigerdirect.com,
www.zipzoomfly.com,
www.directron.com,
www.pcmall,
www.newegg.com,
www.outpost.com, and so on. You can find dramatic savings on them. You want to look at a 4 GB board for memory, and a Front Side Bus of 1000 or higher.
A top quality 500 watt power supply is perhaps critical.
But it seems to me that in building for a family, the critical decision is building for reliability and flexibility... You don't need the grins and jokes that come with a failure.
Upon this solid foundation, I would use onboard sound, ethernet, and video graphics which you can upgrade at any later time. A rugged basic install with a superb motherboard built for the future, gives you choices for the inevitable improvements.
Just remember they are not likely to care what the FSB or component brands are. But they will notice if the memory capacity is inadequate or if the hard drive fills up too quickly because of family photos. Easy access to USB ports and a card reader on the front are obvious choices.
And top it all off with a 20 inch flat panel LCD monitor from Sony, LG, Sharp, or Samsung. Do not try to save money with a junk low resolution, low contrast screen. You also want a monitor that can be adjusted up and down as well as sideways, so it can accomodate a number of users.
There is a good publication on the Magazine racks of Wal-Marts and supermarket chains, called PC Building Bible 2007 which has a number of useful suggestions.
Good luck. Let us know what you decided.