I sincerely believe that the biggest mistake a lot of anglers make, when starting off their potential young fishermen/women, is to go cheap. Nothing will turn off a young angler faster than equipment that fouls up and creates delays & problems. You do not have to spend hundreds of dollars, but trying to get away with a $15.00 combo at Walmarts is just not going to cut it. Not if you want them to enjoy their experience on the water with you and want a repeat outing.
That being said, there are plenty of good quality starting outfits you can put together yourself. I would definitely start them out with a spincasting type reel/rod combo. Pick out each reel and rod just like you were getting it for yourself. Do some online searches for opinions on various makes of spincast reels (the Zebcos are hard to beat these days). Rods you can select yourself by feel at the store. Or online if you are comfortable with that.
Best accessory you can get though is a small colorful tackle box with lots of colorful and "mysterious" lures (plastics & jigs). Along with some hooks, bobbers and split shot of course. Let their imagination go crazy! They'll love you for it.
"A voyage in search of knowledge need never abandon the spirit of adventure."