Hey camshaft, how goes it. You got a Local Fish Store ( LFS ) around? If you do can you manage to get some fish bags and styrofoam boxes? don't feed your fish for 3 days. So, they don't produce waste while you are transporting them. You can double bag your fish and keep them in the bag for a while. As mentioned already, keep 2/3 of the bag air and the rest water. If you can't get a hold of fish bags you might want to transport your fish in a cooler. Buy one of those pumps to keep live bait at the bait shop. Or one of those battery operated air pumps from your ( LFS ) or online. I would net out as much of the gravel as possible and put them in the styrofoam box, buckets, or cooler. Store the filter media in something wet. A bucket, cooler, or plastic bag.
Fish properly bagged without oxygen pumped in the bag will only last a while. Depending on how many fish and size of fish per bag. Check on the bags frequently. If you got your fish in a cooler with air pump they will do better. Put the gravel in the tank 1st. When you fill up your tank use a water conditioner. I use "Prime" by seachem. A capful is all you need for your tank. Install your filtration. Float your fish bags in the tank for about 15 minutes to match temp in the tank. Like you would if you bought them from the LFS. If the fish were in the cooler just add some aquarium water into the cooler till you get about 1/2 aquarium water and 1/2 old water in the cooler. Then toss the fish in the tank. The water with your fish may contain ammonia. I would toss it out and not put it in your tank.