Recycling water is only really feasible for the T500. If using the Alembic Pot Still system, you would need very large storage tanks. Alternatively, if you'd rather not use any water at all, use an Air Still or Air Still Pro which uses air, not water to condense.
During distillation using the Still Spirits T500 and Alembic Pot Still Attachments, you will run a fair amount of water through the still to control the temperature and condense the vapour.
You can recirculate water during a run, however, you would need to find a way to cool the water before it goes back into the still. You can find examples of setups with one big barrel (~200 - 300 L (52.8-79.2 US Gal)) of water with plenty of ice and a submersible pump which is connected to the water inlet of the still. The water is then pumped through the still and the water outlet feeds into the same barrel. You should ensure that it is never submerged in the water. The water is thus recycled, however, they must always ensure that the water temp in the barrel is below 20°C (68°F).
Some people collect water from their gutters around their houses which is at a cool enough temperature to use and run through and, why not if it's just going to waste anyway. As the water never touches the distillate it doesn't have to be perfectly clean water but it should always be free of any debris etc.
Other setups include having 2 x 200 L (52.8 US Gal) barrels and a submersible pump where one barrel contains all the cooling water (200 L (52.8 US Gal) should be enough for a T500 run) and is connected via the pump to the water inlet of the condenser.
The tubing which is connected to the outlet of the condenser runs into the second tank which is empty at the beginning of the run but will fill up with the hot water during the run. Then for the next distillation (or after the water has cooled down below 20°C (68°)), the tanks can be switched over and run again.
If you prefer, you can collect the water you pass through the still from your tap. When it's cool, you can reuse it for any household applications like watering plants etc as it doesn't touch any alcohol, it's simply hot water.