There is no 'best'. You could do quick searches on all of those plants to find out what a lot of people say and then decide which to try. You know: if one opinion is good, a dozen are even better! I would typically use a 50:50 mixture of sharp builders sand and peat moss....or perlite and peat moss. I have also used a very good (meaning porous) soil-less potting medium. What you should NOT use is garden soil or compost or all peat.

I know lots of people that use all sand or all perlite, but I like a little water holding capacity going on. Personal preference.

Rhizo, I have used all your mixtures to root, I still go back to my rooting bead , which is a mix of Garden soil and basic compost. I don't know of anything I haven't been able to root, if I keep it damp. Why should I not use garden soil and compost? It has worked for me. I haven't been able to sale and give away all the plants I have rooted this way. Why is your way the better way?

I'm very glad that yours has worked for you! And I should certainly clarify something. Garden soil and compost work wonderfully IN THE SOIL. If you have a propagation bed located somewhere in the garden, then perfecto! It's just that garden soil and compost turn into something else when removed from the natural system in which they have been a part, and confined in a container of some kind.

I was thinking of a rooting flat or containers, which is how I propagate everything. Garden dirt and compost tend to lose their porosity in containers, and those cuttings need oxygen in order to generate and develop plenty of new roots. Also, those roots need plenty of available oxygen in order to grow strong and vigorous.

Make sense?

I use Pro-Mix for starting seed and for propagation. However, using floral foam (also known as oasis) is an option.
Japanese Maples are mostly grown from seed or by grafting.

Here is a link that might be useful: More about Japanes Maples

Well, I went down to the creek and got 20 more 5 gallon buckets of sandy creek bottom soil. I'm like Tony in that I can root stuff faster than I can give it away. No matter what you use as a potting mix, a combination of bright shade and keeping them moist seems to be the key. Too much sun and dried soil is a sure way to kill anything.

terramadre, I used oasis for a great many thing in the past, with great success! I'll have to find my stash and put it where I can remember to use it.