A softener will remove your iron but, the slime says IRB (iron reducing bacteria) and if you have enough to cause a problem, you must kill it with a disinfectant. It usually shows up in the most frequently used toilet. Use bleach to clean the toilet tank and see if it comes back to any extent; IRB is harmless but can cause an odor in the water.
With your own well, water quality can vary from one side of the road to the other or next door just 100 yards away. City water usually doesn't but 3 miles away, there may be two separate distribution systems or sources of water being used.
Stay away from the big box store brands. They last like 2-5 years and are expensive to repair. And you can't get more than a 1.2 cuft size in a cabinet model. For sizing info, check out the sizing page on my web site.