Nowadays lamb is much milder than it used to be, and can be used in most pork or beef recipes. The leaner the cut, the milder the flavor, as a general rule.
But family-freindly is kabaobs. Buy and trim almost any cut (like I said, as a beginner look for something lean; trim most of the fat off if you're afraid of the gamy flavor. A leg is good for this, but inexpensive 'steak' cuts will work since you're trimming). Cut into either cubes or long, thin (about 3/4 inch wide, narrow). Then marinade the meat in red wine, garlic, herbs (thyme and rosemary would be my choice) for a few hours. If you use bamboo skewers, soak in water for at least 20 min to keep them from burning. If using cubes, alternate chunks of meat with wedges of onions, large garlic cloves, and bell pepper strips, and any other vegetable you like that will stay on a skewer. If you've done long thin strips, you thread them on the skewer as if sewing with a running stitch. Put on the grill ... the long, thin strips will really only take a few minutes per side. The cubes won't take too long either, maybe 6 per side for well done (I like it more rare, but that is an acquired taste).
To make this a complete, fun meal I recommend buying Near East brand taboule and couscous. They are very easy to make up, take no real time, and give an exotic touch to a meal. If you decide to do this, buy lots of fresh parsley for a pretty garnish that YOU EAT.