Dependent on your geographical location, I would obtain a copy of the local guide book and read up first, find something suitable for novices. Its always worth having a few extra bodies around to encourage/help small folk over obstacles, along with a tackle bag that has a few essential items, rope, slings, crabs first aid kit and the like!
Round here (Mendipshire), the snappers have so far visited: Compton Martin Ocher Mine, 5 Buddles Sink, Box Quarry, Swan Mine, Sanford Levvy, Goatchurch Cave, Fairy Cave and Aveline's Hole.
As others have said, "fine tune" your trip don't make it too long, have lots of big boulders to traverse, or in my son's case: too many "scary drops", make sure they have adequate clothing (and something to change into afterwards), plenty of food and drink (this can be used as a "carrot" - on one occaision we took those decoratable gingerbread men underground so they could turn them into "Mine Explorers", my daughter's 10th birthday party was held in the Catherderal in Box complete with cake, glowing balloons, party poppers, and a few small sparkly pyros! ) and re-assure them that at any point if they feel "uncomfortable" that you'll return to surface - after all you want them to enjoy it and come back for more!
Better to regret something you have done - than to regret something you have not done.