A home RO system is a good idea in terms of convenience, but may not be ideal in terms of total ownership cost. In my case, the level of sodium in my municipally softened water was too much for me and my family to handle. My RO system serves my brewing and the family drinking water needs.
RO does use a lot of water to make its product water. Fortunately in a lot of places, water is relatively inexpensive. A consequence of creating a lot of wastewater from the RO process is that the wastewater mineralization is relatively low and the effect on the environment is lessened.
Most RO systems come with a pressure-triggered cutoff valve so that they do not run constantly. When the pressure on the outlet side is high enough, the flow stops and no wastewater is produced at that time. Nate is correct that you do need to have them hooked up constantly. You don't really want to hook up a system, use it, disconnect it, and then dry it out. It should be hooked up constantly to keep the membrane and other filters hydrated constantly. If you have a concern with water use while its 'off', the user can close the inlet valve and then you don't have to worry about any leakage or waste. When you need it, open the valve and everything is still hydrated and ready to go.
If you are storing your RO in a pressure tank, then you can reduce the amount of water waste by including a permeate pump in the RO system. They improve the pressure drop across the membrane which decreases the water volume wasted. Permeate pumps are noisy though. They produce a cyclic thumping noise that might not be welcome if its in your living area. The other option to improve water efficiency is to pump your water into an open tank. That way there is less back-pressure on the membrane and that improves the efficiency. A simple float switch in the open tank can shut off the flow and avoid an overflow. Of course, you have to move the water from the tank yourself.
RO does not produce pure water. There is a little bit of mineralization that passes through the membrane. It depends on the ion, but there is typically between 1 and 4 percent of the raw water's ions that make it through into the product water. A typical RO water profile is included in Bru'n Water.
A RO system should use a good membrane and it should not be a proprietary unit like GE, Kinetico, or Whirlpool if you want to keep your ownership costs low. The generic systems that include a name brand membrane is generally going to provide you with the same life and service. A good brand name for membranes is Filmtec or Dow. Look for those names when scouting for a system. Ebay has a bunch of system providers and the internet is full of providers. All the components typically come from the same suppliers and they typically have quality.
A RO system MUST have an activated carbon filter to remove chlorine and chloramine. Those chemicals will quickly destroy most membranes if left in the water. A good RO system should include particulate filters to keep grit and debris off the membrane and carbon. I typically see 1 and 5 micron filters quoted. A RO system might have a polishing activated carbon filter, but I don't really see the need for that since the raw water went through carbon once. So, look for a system that says it has 3 or 4 stages. A 5 stage system may be overkill since that typically includes that second carbon filter.
If the raw water feeding the RO unit is really hard, then it might be helpful to feed the unit ion-exchange (salt) softened water to help extend the life of the membrane. If there is already a softener in the house, then feed the RO unit from the softener. If you don't have a softener, don't fret about it. The high amount of water wasting is intended to help avoid crusting up the membrane with mineral scale. Feeding the unit hard water isn't a big deal.
Do have a way to check the quality of your RO product water. A TDS meter is a good idea for anyone using RO water. That includes anyone buying RO water from a grocery store machine. I've seen multiple cases where brewers has problems with their brewing only to find out that the RO water machine was having problems and was delivering untreated water. The TDS meter is cheap and its your first line of defense against a problem with either your home unit or grocery unit.