The orchid is a Trichocentrum cross of the two hybrids named after TRCTM. You can repot it in plastic, now or in the early spring is okay. I wouldn't mount it because it will probably get too big for mounting as it gets older.
Either a bark mix or the CHC that it's currently in should work fine, but I'm leaning to the bark if potted in plastic.
Good luck. Post pics when it blooms.