Hi Camille,
What fun to visit and share the magic with your grandchild!
16 months old is a time when every experience is magical. But also, it is a time when loud noises, dark places, bright lights or big 'characters' can be scary.
I think the Magic Kingdom is the place to start! Here, the parades would be appealing. Parades are usually in the afternoon (eg, 3pm at the Magic Kingdom). If your grandchild is still sleeping in the afternoon (which I am guessing is likely), you may want to make sure you head back to your resort before that (say by noon) and then come back to the park for the parade. Check out this link to find out when the parades are :
Magic Kingdom
Young children are most often afraid of the bright lights and loud sounds of fireworks, so you could easily cross these off your list and be home for an early bedtime.
Gentle rides will be the way to go...like 'It's a Small World' and 'Cinderella's Golden Carousel' (sit with him/her on a bench seat, or hold them on a horse if it is not too scary). Dumbo the Flying Elephant would be fun too, as long as the height would not scare him.
One of my all-time favorite things to do to let little ones run around in a relaxed area is 'Tom Sayer Island'. Take a 'raft' over to the island and explore for hours.
I would also recommend renting a stroller as you enter the park - he will be able to rest or sleep when needed. I hope this helps. Have a truly magical family time together!