What you do with an RO system depends on, of course, how much you want to spend, how much water you want when and how much tinkering you want to do. If your brewing requirement is modest then you can indeed collect water from a 'home' system over a period of days and collecting it into a rain barrel is fine (as long as it is clean and free of plasticizer or anything else that might stink up the water. At the other end are 'whole house' systems that supply the water from a higher throughput unit to an atmospheric tank from which it is pumped into a pressure tank or directly to a pressure tank. These are just like the bladder tanks used with wells except that they are made completely on non metallic materials as RO water is quite corrosive. With such a system you can pipe the water around your house/brewery just as you would well water provided that the plumbing is non metalic. As PEX seems to be becoming so popular in houses these days this should not be a problem.
The low $ home systems are inefficient with respect to water collected vs. water wasted and many run at less than 20% (4 gallons wasted per gallon produced). This is done in order to obviate the necessity for softened feed water. With softened feed water and suitable RO system configuration (pump and concentrate outlet throttling valve) efficiencies up to 50% and a bit above are possible. With a feedback valve (some of the concentrate is fed back to the input) efficiencies of above 80% are possible with the cost for that being somewhat lower rejection (i.e. more ions in the output stream).
With low volume, even low volume with high efficiency, waste is not a problem. If you are a large brewery putting out a large volume of concentrate at 5 times the TDS of the supply water your municipality may have a few things to discuss with you but for the few gallons that even an active home brewer produces the concentrate load on the waste water treatment plant won't even be noticed.
There is no more problem with storing RO water for a long time than there is with well water. I would think nothing of drinking water from my well's bladder tank after being away for 4 months and I would think nothing of drinking water from my RO systems bladder tank after 4 months absence. I do drain my atmospheric tank, however, and its vent pipe is protected by a screen which prevents the entry of bugs.
As the title is 'Let's see your RO setup' I include the following link to a photo:
http://www.pbase.com/agamid/image/124857348
Please understand that this insanity was the result of a retired engineer just having a ball doing a home brewing project and that lots of the stuff in this system isn't really necessary. The skid, at the right end of the bench, is the essential device and can produce 500 gallons per day. This was sized to allow me to collect the 200 gal I need for a typical brew day in a few hours. The system also supplies my lab.
Intermediate sized (GPD and bells and whistles) systems from the reef aquarium hobby are very popular with home brewers. I sure someone will post a link to one of the supplier's website.