Chaval coat questions re: underlining and interfacing

I'm excited to make this coat. It will be my first coat and first Leisl pattern. I'm using a silver and blackberry wool tweed (see attachments). My questions: is there any benefit to using an organza underlining where interfacing is not used? (I've underlined dresses with great success, but maybe it's not important in a coat??) and does anyone have a recommendation about interfacing type? This fabric is not very stiff (see photo)but I don't want to remove too much flowiness. I've tried the shape-flex woven cotton on a sample and am concerned that might make it too stiff. Any thoughts or experience with similar fabrics?