The style you like seems to be cantilevered into the wall for stability - depending on your available options you can use solid wood - but the more stable option is to clad it ! Just remember that not everyone likes the way that it's seems very open - so may limit your buyers if you plan to sell in the future !

I wanted to know which all Italian marbles are best suited for exterior cladding?

Would like to suggest you to go for Natural and local as far exterior cladding goes.

Hi Notin, I hope you are doing fine. Exterior claddings need to be durable and long lasting since they exteriors have to face weather changes, wind and dust and constant heating and cooling. Stone is the best material for exterior cladding, specially for weather like India. Stone has a property to insulate the interior spaces keeping them cool during the summers so your AC bills will be less over the years. Also stone is cheap in cost and readily available. Installation is not a problem and you get variety of designs and material finishes in stone cladding.