When checking for anemia, start with red blood cell count, hemoglobin, and hematocrit. Then look at MCV and other red cell indices to measure average cell size. Check iron studies including ferritin, but watch out: ferritin rises during inflammation, so it can hide real iron deficiency.
Usually when you're looking at anemia, you're looking at the current amount of red blood cells, so the number, and also the amount of hemoglobin and the hematocrit relationship to each other, looking at the mass of red blood cells. Look at the indices, which start with a big M, so like MCV and all the other M numbers. Those are related to the average sizes and efficiency of the red blood cells. Then you usually look either at the iron binding concentration like TIBC, UIBC, and you ought to be looking at ferritin, which is stored iron. One thing with ferritin is it can go up when you're inflamed and you may not have high stored iron, but you might be inflamed. So it's a good marker, but something to look at there.
