I moved my tank a lot. What I recommend is one bucket for fish/inverts, one (or more as needed) for corals. I would save some of the current water to use when you get the tank to the new house, I always kept around 50%. Starting with all new fresh water sounds good but can cause issues with recycling. Leave just enough water in the tank to cover the sand but more than you think because you'll want to suck out the detritus that is stirred up after the move.
After everything is in the buckets snap the lids on throw them in the car with the tank drive them over. When you get to the new house place the tank, add some water, unpack corals, then the fish/inverts. Top off the tank.
Your move shouldn't be long enough that you need to worry about having heaters/air pumps in the buckets. I moved one of my tanks from KY to MD in a cooler with no air pump or heater.