OK, I'm a geek. So, before anybody reaches for the "I don't advise you to do this" button, Yeah, I know. And I'm going to do it anyway.
scenario:
VERY rural western Kansas town. Pop. 2200. Has own internet provider, offers webspace, but really doesn't have technical capabilities.
However, offers pretty darn good dsl service. Will supply static IP. Other entities self-host here, as well. Library, city.
relatively small congregation, but with a large (relatively speaking, of course) target audience/market/mission field (however you're comfortable thinking about it!) in the community.
So, not really looking at "world wide" exposure, just looking at being a good usable attractive website for the community. Shouldn't be very high visitor count. So I've decided to explore self-hosting.
What is the minimum and recommended processor speed I need to run Linux/Apache/Typo3/WEC? Minimum and recommended RAM? A spare computer here at the church is 500mhz, 132 RAM. I know it's not much, but would it be possible to start with this?

Visit: http://wiki.typo3.org/index.php/Typo3_Installation_Basics#System_requirements
WEC is based off of Typo3 so it should help to check there first.

That server 533,mhz would be a little slow ...
My suggestion would be at least a PIV 3.4Ghz or higher 1 - 2GB Ram.

You can get these pretty inexpensive and linux friendly as well.

Bruce,

Here is what we suggest on the WEC website:

http://webempoweredchurch.com/gettingstarted/hosting/

which is basically what Glenn said with a few more details. At a minimum, you would need more RAM if the motherboard can accept it. Then you just need to see how slow it feels.

In Christ,
Mark