I would think that licorice would be first choice as it is very specific for supporting and nourishing the adrenal glands. The drawbacks to using licorice are: 1)it can raise blood pressure in some people, so if you already have high blood pressure it is not a good choice; 2) I have seen it raise blood sugar levels in a few diabetics; 3) it is estrogenic so if you are male, you do not want to use it long term.

These side effects take extremely high doses over a very long time to occur. For example, it takes around 50 grams of licorice daily over 6 months of continuous use to raise the blood pressure.  That would be one entire bottle of 100 capsules for over 6 months.  Most people will never get anywhere near taking that much licorice root.  And this side effect can be countered by the addition of high potassium containing herbs.

The estrogenic effect also requires doses that most individuals will likely never reach.

I am not familiar enough with Ashwagandha Root to comment on it.

Ashwagandha is a very good adaptogen.  It actually has a calming effect through the activation of the brain's gamma amino butyric acid (GABA) receptors.  Ashwagandha also helps to support the thyroid by increasing T4 to T3 conversion.

 My vote is for siberian ginseng.

I agree, it is a very good adaptogen.  Although adaptogens are best taken in formulations for both synergy and balance.

My experience is that is a life saver. It really helps me when my cortisol is too low and the effects are definitely felt within 30 minutes. The effects are tremendous to me. I'm not sure why I can feel it working so soon, but I have for the entire years that I have been dealing with this illness. It's the one supplement that has been working for me without any stimulation. Sometimes when I take licorice it stimulates me. Licorice is good though.

Chinese licorice root (G. uralensis) is calming unlike American licorice root (G. glabra), which has a mild stimulatory effect.