I just moved 13 tanks. I remove the rock and water and leave the sand. Some people say to remove the sand, I never have. In the last 5 years I've moved 30 tanks. I am never ever EVER moving again.
Things to have on hand.
Lots of water.... lots. For the travel containers and the tank when it lands at your house and more.... cause you'll misjudge. And you'll want spare for emergencies.
Buckets. 5g, larger Rubbermaid's for rock and/or large fish (but don't put together).
Maybe some heaters if it's too cold where you are, but be careful of them in small containers. I personally just use a toasty environment, but I live in California. The heaters would make me nervous in a 5g bucket.
Airlines + rigid tubing for every container and enough air pumps for at least every other container. One pump can usually cover 2 containers with a "T". So have more than enough pumps, airline, extra batteries, "T"'s and valves.
Ammonia blocker just in case.
Filter floss the catch the debris when you set it back up.
I would remove the water from the tank into the container with some new, clip on an airline, throw in a couple of fish, secure the top and off we'd go. Some tanks were re-setup in the morning and the fish were back in by sundown. Some fish stayed out overnight. It's been reported that you could experience a mini cycle. I have never had that happen.... ever. I've never lost a fish due to that in a move. But do whatever makes ya feel safe. I always constantly check parameters and keep "ammonia blockers" on hand. But I've never had to use them. What kind of fish to you have?
I would think trying to move both tank and stand together would be risky. Glass or acrylic? If it's glass, don't do it. If it pops off the stand just a bit while you go over a bump, it may not lay back down perfectly. This is common in earthquakes and causes the front panel to just slide right off.
I'm sure I'm missing something...... oh, if you have venomous fish, don't use black buckets where you can't see the fish. It makes it difficult to safely remove them. That's my lesson from the last move. O.O