Thanks for the question.

Before actually answering your questions, and regardless of whether you use rock or wood mulch, there are two important points to keep in mind.

First of all, do not put any type of plastic or fabric under the mulch. This can reduce the amount of water getting to the tree roots.

Secondly, do not apply mulch right up to the base of the trunk. Rather leave about a five inch or so diameter of bare soil right around the base. This will facilitate water getting directly to the roots near the trunk.

While there are advantages and disadvantages to both forms of mulch, I believe that the consensus among most gardeners is organic (for example, wood chips) mulch is preferred over rock mulch. See the following for more information regarding this:

https://blog.davey.com/2017/05/landscaping-pros-and-cons-of-rocks-vs-mulch/ - :~:text=No Benefit to Plants%3A Rocks,spot for weeds to grow.

https://reddilawnmaintenance.com/blog/landscaping/mulch-vs-rocks

https://blog.gardeningknowhow.com/gardening-pros-cons/bark-mulch-advantages-vs-rock-mulch-advantages/

https://extension.umn.edu/trees-and-shrubs/fertilizing-evergreens - mulching-evergreen-trees-and-shrubs-1340014

Thanks again for your question.