Are clay bricks a no go? They are super heavy and it's what I have. How will they compare to concrete? I lined my stove with the clay bricks and I don't know what these lightweight gray bricks that were lining an old basement are but would they work? Thanks!
Clay bricks should work excellently as thermal mass and facing. If they are distinctly heavy and hard, they are likely to be modern bricks which would not adjust well to being in the flame path, but I don't see you using them there.
Your lightweight gray bricks are a puzzle; I haven't seen or heard of brick like that. I would suspect insulating firebrick, but lining a basement doesn't make sense. At any rate, lightweight ceramic items are very likely to be insulating, and not what you want in the thermal mass, except near walls or floor where you are concerned with overheating adjacent surfaces. They should be very good for that.