Hmmmm. Sounds like a phalaenopsis. I would get it out of the sphagnum moss which will kill the plant in 6 months in my experience. Way too easy for the roots to rot and tricky to get the watering right in my case. The roots want to be moist but not soaked. Don't ever let the pot sit in water. I have a big problem with the ice cube thing. Way too controversial. Some people swear by it but others say it's crazy. I won't go there.
Louise, I would replant in the same clear pot and I'd use a bark mix if I watered once a week or clay pellets and perlite (or sponge rock, bigger perlite) mixed if I watered more. Another possibility would be to line an open mesh pot like the one you like with coconut husk fiber then fill with your medium. If it's a phal they don't like to get their leaves wet. You need to water the roots below the crown. I don't repot orchids unless the medium is breaking down or the plant is crawling out of the pot. I let roots grow in all directions out of the pot and hanging down. Some of the roots of my phals grow straight up. I mist them daily till the velamen turns green. I hope I haven't totally confused you!
If I were starting out, I would watch all the video links on the right side box of this cubit pronto!
