For the most part, softeners are pretty simple. Softening water works by exchanging positively charged ions with sodium ions.
Because softeners backwash periodically to recharge, they have a timer (and sometimes a meter) to control when this happens. One of the problems with a mechanical unit is when the power goes out, the time freezes, and just picks up where it left off when the power comes back, so it will start backwashing at strange times - most (if not all, now) electronic timers have battery backup for the time. Electronic ones have been in use for 10+ years now, and are quite reliable now. If you use a metered timer, it will regenerate during the night only after using a certain amount of water, so it wastes less brine (salt) water.
Get one that is easy to service. Although softeners only have to be rebedded about once every 10 years, it should be possible to turn a bypass valve and disconnect the softener. I've seen some old units where you actually have to cut the plumbing to disconnect them, although I'm not sure if those are still on the market anymore. You don't want one of those.
Pay attention to how it is connected: All of your hot water should be soft. Outside taps should be hard (you don't want to water your garden/grass with soft water), with perhaps the exception of a hose in your garage for washing cars. Some people leave their kitchen cold water tap hard, so as to reduce the amount of sodium they are drinking and cooking with, but this partially depends on preference and partially on the amount of hardness (and thus amount of sodium being added). Obviously this is a bigger concern if there are people on low-sodium diets in your house.
Personally, I would avoid electronic/magnetic softeners. There has been some evidence that this can help with very low levels of hardness, there is a LOT of junk out there.
I used to work summers for my dad who ran a water treatment business. We replaced one of these electronic softeners (it had wires going from each end that wrapped around the pipes) with a real softener one time, and took the electronic one back to play with. We tore it apart, and could not find any active electronics in it except for the ones that drove 5 LEDs on the front that flashed back and forth. We hooked the wires up to an oscilloscope and all it was doing was alternating between about +10 mV and -10 mV, with almost no current. I can't see how this possibly did anything -- and the home owner was replacing it with a real softener, so what does that tell you..
Water softeners do use water to recharge, but it shouldn't be that much. With a new filter and all electronic controls working, most systems should send no more than 25 gallons through during a recharge cycle.
The theory is that the filter media (special polymer beads, often stored in what looks like a high-pressure air tank) is "charged" with a high amount of sodium ions from the rock salt you load into the bin. Hard water containing calcium and magnesium carbonate, which are only slightly soluble and cause lime scale, comes into the filter from the house supply, and the sodium replaces the calcium, forming highly water-soluble sodium carbonate in the water supply, which won't cause scaling, leaving the calcium and magnesium ions in the filter. To "recharge", the softener fills the salt bin with supply water producing a brine, which is then flushed through the filter media. The sodium replaces the calcium and magnesium in the filter, which then hitch a ride down the drain as soluble chlorides.
The amount of water needed to produce the recharging brine varies by manufacturer and age of the filter media; this ion exchange does take its toll, as the charged ions are corrosive (a surplus of positive ions in a water solution makes the solution acidic). The softener also relies on several detectors to determine system status, that are exposed to hundreds of thousands of gallons of water over their rated life, much of it salty and highly corrosive. Over time, all these components wear out, with more or less detrimental effects on the system's overall efficiency.
Best Answer
This is the salt water brine tank that is used to let salt set in the water to make brine which is then flushed through the resin in the softener before being rinsed to the drain. So a bunch of things are good to keep in mind as this is not a hazard. Most molds, especially those which form in water are not hazardous, only a few which we might breathe the spores. This is not what you drink directly but only what is used to reset the ion exchange. Salt is, in itself, used to delay bacteria, as in treating meats like ham or salt pork. The chlorine in the water used to make the brine will kill most harmful bacteria as it does in the normal water treatment.
I would suggest cleaning as a way to make it "feel" better, even though it is mostly just dirt, possibly from using less clean salt like perhaps blocks of stock salt. Then the barrel should be topped off with salt to allow it to make brine as at the current level, the softener is not going to have enough brine to operate. To avoid doing it more often, I like to nearly fill the barrel.