A Fleck 5600sxt Metered 40k system and a Big Blue sediment pre-filter is a good choice for your application. 9lbs salt will give you 27k capacity and cycle every 7 days.
At 12 grains of hardness and 300 gallons per day usage, left untreated this family would experience 187 gallons (7000 grains = 1lb) of dissolved rock flowing through their home in 1 year. That is why it needs to be treated by softening.