The special Fabric Crayons tell you to draw the picture on paper and then transfer the design onto the fabric with the iron. I have done this and found the pictures a little too light. Always added more color after the transfer.
You can use regular Crayola Crayons on fabric. The key is that the fabric should be a non-printed (muslin I think is best) because the crayon will not go onto a print evenly. Then you have to iron off the extra crayon wax between paper towels or brown paper. (kind of messy).
There are special fabric markers that work like felt-tip pens. One end has a finer tip, the other has a brush. These only need to be heat-set.
Pigma pens have a fine tip and I don't think kids would like them as much. They also have to be heat set.
Some people use Sharpie colors but it says right on the package - not for fabric, so I don't use them on any fabric that needs to be washed.
I think the hand print outline is a good idea. You maintain a bit more control over the project that way. Trust me, it can easily get out of hand. Have fun.