If it is possible to move everything from the old house straight into the new house that would help. You could save the fish for the last thing. It also depends on how far you are moving and how long the drive is. Considering a short distnce (30 minutes or less) I would proceed as below.
When you're ready to move them, fill buckets with tank water, put the fish in and cover with lids. Make sure the buckets aren't too overcrowded with fish as they will deplete the oxygen too fast. Save all the water you can as the water at your new home may have considerably different parameters as what you currently have (higher/lower pH, ammonia/nitrite/nitrate in the tap water). Putting the fish back into the water they came from will help ease their stress. You wouldn't hae any problems simply topping off with the new water. That would be equivelant to a normal water change.
Quickly take everything out of the tank and bucket it too. Make sure you keep your filter media wet at all times. It isn't necessary to get every bit of substrate out, just enough to make the tank light enough to carry. You don't want to leave too much though and have the weight of the substrate cause the bottom to crack in the move.
Once everything is loaded and transported to the new home, open the buckets and add filtration or aeration and a heater if possible. Watch to make sure the fish don't jump out. Set up tank, add substrate, plants, decorations, etc. and put water and fish back in. Depending on the type substrate you have, you may want to wash it. If it is gravel, I would rinse it to remove any debris and waste that is in it. Sand shouldn't be as big a problem but could still be rinsed. Rinsing substrates made for planted tanks, such as Eco-Complete and Flora Base, may not be wise as you my wash out some of the nutrients they contain.