Question
about how many inches deep should my substrate be for smaller types of orchids around 12'' tall?

Answer
Rich, I recommend that you use a well drained pot and put a bit of crocking in the bottom. Then I would insert the orchid roots into the pot following by the potting mix.  That way, there is less opportunity for the roots to move downward.  They would do best to be able to grow to an anchoring surface which may be lateraally to the pot side.  In short, aloow to roots to be as close to the pot bottom as possible.  Some potting mix may drift into the pot bottom and that is fine.  I just would not try to create a layer of potting mix at the bottom of the pot which might impede air flow.