Tank moves can be stressful but not all that hard with some planning. Well you first need a number of 5g buckets with lids. You will also need some airstone, air tubing and a air pump or two. Fill each bucket with tank water, and I'd put 1-2 fish per 5g bucket. I would also scoop out your gravel and put some of it in a 5g bucket with a little water too. Some of the gravel can be rinsed and cleaned, but you will want at least some of it so that you avoid a full cycle on the tank.
Since its freshwater, you just need to keep the fish water buckets aerated while they are waiting, but they should be fine without aeration during the drive up. Once you get them up to the new house add the aeration back to the buckets, and they should be good for up to a day or two like this while you get the tank moved and setup again.
Setup the tank at the new house, get it up to temp and everything. Add and plants back first, and then once ready you can add the fish back.
Also I would move the tank as the very first thing if you can. Get it moved and setup before you start moving anything else. This way the tank will be coming up to temp and stabilizing while you are moving the rest of the house, and then once you are moved it should be ready to add the fish. You can also move it as the very last thing, but generally you are pretty tired by then so it can be a bit more difficult at that point. Just dont move it during the middle of the move as it can complicate things and usually just adds more stress to you and the fish ime