Fortunately for my family, I am the one who designed and maintains the family reunion website. I am also the webmaster of another branch of my family. The webspace and domain name fees are relatively inexpensive. I use Yahoo Geocities. See http://geocities.yahoo.com/. They offer free webspace, but you have to deal with those annoying pop-up ads with the free service. There are other companies who offer webspace and domain names for reasonable rates. Also, see www.bravenet.com.
Keep searching for someone in the family who does that type of work. He or she may not mind doing the website. Actually, I find putting together a website enjoyable, so hopefully you will run upon a similar person in your family. Keep asking around.