I design industrial water purification systems for a living. Softening removes dissolved calcium, magnesium, and low levels of iron from water, but in turn increases dissolved sodium levels, which comes from the salt used for regeneration. Too much sodium can be bad for you, but your water is not very hard, so the amount of sodium will be small in relation to that present in food.
Eventually you may have to chemically clean the softener resin if it becomes iron fouled.
There are filters which use natural or synthetic geensands and remove most forms of iron and manganese (even at much higher levels) without softening. They typically use potassium permanganate (or sometimes bleach) for regeneration. I prefer the type of iron filter which regenerates intermittently instead of continuously, as it is less likely to put residual chemical in your water. Mechanically, they are very similar to a softener and cost about the same.
Softener resin has a softening capacity of about 30,000 grains of hardness per cubic foot. At 4 grains per gallon hardness level, you will be able to soften 7,500 gallons of water (per cu. ft. of resin) between regenerations. It takes about 15 pounds of salt to regenerate one cubic foot of softener resin.
Whichever way you go, triggering regeneration with a water meter (vs. a timeclock) is more expensive to buy up front, but more efficient in the long run, as it saves both chemical and regeneration water.