Welcome to GoY, Ladyrocker!
If it is in a plastic pot, the roots will make bulges in the pot when it is ready. If a terracotta pot, the roots are likely to break it. If a stoneware pot, the rule of thumb is to transplant when the plant is 4 times as tall as the width of the pot.
As for the best medium, I prefer cactus mix, myself.
Hope this helps!

If you cannot insert your finger down to the first knuckle, it's most likely pot bound - time for a bigger pot. There should be at least a half inch space between the rootball and perimeter. I've had a couple terracotta pots explode on me because they weren't going to wait for me. Of course in the middle of the night -and it was scary as heck.

If this is related to your other question about a plant being pot bound, the best place for the white Bird of Paradise is in the ground. I grew one from seed, and it took 11 years for the first flower. By then it was around 15 feet tall. All the offsets have been that tall when they started flowering. But site it carefully: The roots go deep and it would take heavy equipment to pull it out. Mine isn't going anywhere, and I haven't been able to dig out a side shoot. Mine is starting to flower and will have about 6 flower heads on it.