I've seen many mixed reviews on Sourdough and Breadmakers. Many think it doesn't work, some think a breadmaker can be manipulated to make good sourdough and others have "fantastic" recipes for breadmaker which include adding both sourdough starter and baker's yeast (why both?).
I don't have an oven so breadmaker it is. No questions there. I live in a studio apartment with small kitchenette which has a microwave and hob. If I want to make anything more "sophisticated" I rely on sandwich maker, george forman grill and breadmaker.