^Hrm. Been evaluated for other kinds of anemia other than iron deficiency, or for some kind of hidden blood loss? Very important...
Yes, taking just the iron supplement on an empty stomach with orange juice is best -- don't take with other multivitamins as the calcium with interfere, and wait a couple of hours to drink coffee, tea, or milk. Get enough vitamin C? Also, vitamin A deficiency can contribute to anemia, so be sure to get those yellow and orange fruits and veggies -- it's the inside color that indicates beta carotene, the precursor to vit A. Not so hot on Vit A supplements as you can overdose on those, but not the precursor carotenes.
Whole grains can help, but sometimes going gluten-free is necessary, with even slight gluten intolerance.
And you might just be one of those people who needs to eat beef, though it's always good to try to stick to the healthier cuts like brisket. The kind of iron in meat (heme iron) is much, much more easily absorbed than the vegetable source kind.
Sorry for the nutrition lecture.