Whole-home system: The only ongoing task is maintaining the salt levels in the brine tank. Check the brine tank monthly and add a bag when it's low. Salt bags are available at Home Depot or Lowe's for $8–10 per bag.
Reverse osmosis system: Replace the filters once every 12 months. There are 3 filters total and the complete replacement set costs $150.
That's it. No complicated upkeep, no proprietary service calls required.