What kind of mushroom goes well with Tandoori Chicken on a pizza?
Not the question you asked, but properly done tandoori chicken or Mexican chorizo will completely mask all of the other flavors you list.  Subbing a simple grilled chicken and Spanish chorizo makes for a nice savory pizza (indeed, I had just that pizza last night, without chorizo).  In that case, simple white, button, or crimini mushrooms (the latter sometime sold as "baby portabello") will give a nice earthy note without breaking the bank.   Saute' them before putting them on the pizza for maximal flavor and minimal chewiness.

As for herbs, basil and oregano are obvious, and nothing else is required.  Marjoram and/or nutmeg would be okay. Lemongrass would be interesting but maybe overkill.