If you do get a dehumidifier (total god send IMHO), it's not a bad idea to put them on the first floor landing, as the moisture will tend to rise. There are 2 types - Desiccant and Refrigerant. Refrigerant ones don't do nearly as well anywhere that gets cool, but can be more powerful for their size and cheaper to run (slightly), as long as it's warm.
Is it a new or an old house? Old ones tended to never really be that air tight, so you get damp getting through the brick work, and modern ones are so well sealed you never let it out.
Also - check your gutters - very easy for a blocked or not right one, to get a wall damp, and they soak up water like you wouldn't believe, which then slowly boils off into the nice warm inside.
In terms of insulating the water softener - yes it's a good idea - water from the air can only condense on the first surface it meets, so insulating it will allow a bigger heat difference and it'll be less cold - so less pooling.
Rupert