Brea, it probably is a good idea to re-pot your Phal once the blooms are finished, but that may take a couple of months - yes they're slow growers and slow bloomers but once they do bloom, those flowers last a long time!
As far as a pot, for growing indoors a clay orchid pot is probably your best option. They are available at any big box store (HD or Lowe's) and not expensive. Just be sure you get one with the extra holes in it - orchids really like lots of air around their roots as you can see from your present one!
When you go to get your pot, also buy a bag of "Special Orchid Mix" or "bark mix" or sometimes they even have it labeled "Phalaenopsis Mix". It's chunks of bark, charcoal and perlite, just the right stuff for Phals to attach those roots to. There are good directions on the bag, but here's also a link to the American Orchid Society's culture sheet for Phals:
http://www.aos.org/Default.asp...
One thing they don't say in the potting directions (bottom of the page) is that when you set your plant in the new pot, be sure the crown is at an angle so that water runs out of the cup of leaves. Having any water sit in there is a risk for crown rot disease that can kill your plant pretty quickly. Phals are naturally trailing plants and the flowers are meant to cascade downwards, not stand up as you see them in the store. (I think they do that so they can ship a lot more plants in a box without breaking the flower stems, but
) Here are some of mine, crowns at a slant.
We love questions, and enabling new orchid nuts like us to feed their plant addictions . .
You have no idea how excited I was when I saw that shoot starting to grow!!!! I hope I get lucky and see another!!!!
