It's a beautiful plant, Jolana. I'd advise you wait until the blooms are all finished before doing anything. Phals can be sort of fussy about any change, so let it get acclimated to your home, enjoy the blooms (they might last weeks more!) and then think about repotting it later.
You can buy a bag of that orchid mix called "Phalaenopsis Mix" at HD or Lowe's, and a clay orchid pot with some vents in the side might be a good idea, too. You're right, it does look just like mulch, but that's what orchids like. Remember they are epiphytes that grow on trees in nature, which means they absorb a lot of nutrients through the leaves as well as the roots. They really like their roots to get lots of air, so that they dry out after watering, too.
