I did a quick google using the term 'recipes cut out fat' and found a bunch of sites like this. So that's a good place to start for substituting low fat for high fat ingredients.

If you have trouble with anemia, you might try cast iron which leeches iron into your food as you cook it. (This tip is anecdotal from a friend who used cast iron and her doctor told her that was why her iron count was so high.) If you season it right, you don't need much oil in the pan. If you can only buy one, then a cast iron pot for soups would be my first choice.

If you eat meat, try buffalo (or beefalo). Apparently very low in bad cholesterol-raising fats. I don't know if this translates to all fats. Chicken and turkey are very low fat, esp. breast meat.

Learning to cook can be a pain but if you get a basic how to cookbook and try a new recipe once a week, you'll pick up the general theory pretty quickly. It's all mostly 'how long do you cook stuff until they're tasty/bacteria killed' and 'how does this spice thing work anyway', with bonus 'a good sauce/gravy/salad dressing' makes everything taste better.

Good luck! :-)