We are a military family and move often, lol, so this is one topic I can discuss with some experience.
Since it sounds as though your move will be a relatively short distance one I would do the following:
*move everything else first and save the tanks for a time when you can concentrate SOLELY on moving and re-setting them
*obtain either large storage tubs or, better still, coolers (coolers are insulated so there is less risk/worry of temperature changes). Non-seethrough is better as the dark interior is less stressful for the fish. Also, an advantage over buckets, they are lidded so you can reduce the spillage during the transport
Keep weight in mind when selecting containers - bigger isn't necessarily better as bigger will also be HEAVIER with water/fish in it and you may find yourself unable to lift/move the container when the time comes.
*fill each container approx 1/3 full with water from your tank - this leaves ample air space for short moves with the lid in place during the driving/carrying time.
*place the fish, plants and filter materials (if applicable/practical) in the container/s (if you are moving lots of fish and plants you may want to separate the two as the fish will likely be quite panicky and could damage the plants with their swiming about)
*drain the tanks (some people suggest moving them w/water as long as it isn't "much" -ie less than 1/4 - but it isn't worth the risk of seam strain to me. Using additional containers will allow you to preserve as much original tank water as possible - minimizing the amount of "new" water you have to use to fill tanks at the new location. Aim for a minimum of 50% old tank water - more is better.
*move all tanks, equipment, fish etc to the new location (use appropriate climate control in the vehicle and new location to minimize temp fluctuations)
*set tanks back up, fill at least 1/2 w/old tank water/new water ...... basically to a point that will be where you will finish filling with the water the fish are in
*make sure all equipment is working - let temp stabilize, etc - also monitor tanks for any leakage
*transfer fish -- I find it best to keep the tank light off for a bit (usually we are in the evening hours at this point anyway so I leave them off for the night) to allow everyone to just have some "quiet" time to re-adjust