If you want to try transporting the tank with substrate in place (I have a number of times), the issue is the torque that is placed on the tank as it's lifted/moved - if you can slide the tank onto a sheet of plywood & have decent assistants, you'll be fine. If you're on your own, I'd just scoop out as much of the ADA as possible.
OTOH depending on the plants, as you remove them there may be considerable mixing of the substrate & then you might as well pull the substrate, it's just easier/safer.
Depending on the type of plants, they may transport better submerged in water -re physical damage/bruising of softer leaves.
Fish - you want 1/3 water to 2/3 air whether they are in bags or bins; if you have a battery air pump, use that in the bin BUT realize that in a closed system, there is still limited oxygen.
Depending on the fish types, I prefer to bag - if your local shop has the breathable bags, I'd use those (but you need to be careful with stacking).
When setting up for transport, I do a "water change" - this may be a bit more involved as it's not currently your tank, be prepared to add ammonia adsorbing chips to the bags/bins (not sure how available there are in your area) as well as Prime (I prefer this over Amquel ... back when, Seachem had data available for using up to 10X amounts of Prime & effects on ammonia, nitrite, nitrate, fish; having never seen similar studies from the manufacturers of Amquel, Prime was an easy choice for me).
Filter - give media a quick rinse in treated water (no need to use tank water) to remove debris, then just transport damp in filter with a couple cm's of water at the bottom & filter closed as normal: in this state, filter bacteria are stable for days/weeks/months ... as the time extends, the bacteria will go into a "lag" phase but will quickly come back.
When re-setting the tank I always do daily water changes, this will remove organics from any plant damage, from the substrate disturbance, from fish stress, limit ammonia/nitrites etc in case of unexpected filter disturbance.
Rinse/scrub hoses clean before re-setting the tank.
If it's a long day or you want to take your time rescaping, just run the filter on a large bin with fishes once you get them home - as long as they are in the dim & in a quiet corner (some fish are very stressed by vibrations re movement near/over the tank), fish will be fine.
In terms of fish health, external parasites which are part of the normal "flora" of fish, will increase significantly with fish stress, so you might consider adding a treatment for external parasites to the holding bin once you have the filter up & running; note that any of these remedies will sequester oxygen & will have some affect on filter bacteria, so this is always a consideration.
It's also essential to be able to observe fish activity/behavior whenever using any treatments, so unless your bin is translucent, I'd not use any medications.
During transport, you want the fish on the cool side rather than the hot, water will have more available oxygen, bacteria are slowed (re that normal "flora").
I don't worry about transporting tank water, but you should know how your tap water compares to the current water or if tank is run with RO etc.
Don't feed fish for at least 24 hours before and after transport, if you can't resist feeding, then be very stingy with the amount.
Depending on the state of the ADA substrate, you may want to gently rinse as you place back in the tank or do some gentle siphon cleaning if you decide to leave in place.
Don't add the fish back in until you're ready to be out of the tank.
When netting the fish for travel etc, use the slow technique rather than any "chase" - again have your bags/bins ready with the mix of tank/tap water before you start netting fish.
Dropping the tank water level before netting helps with "capture", if there are lots of stem plants, just trim these at the base & remove before starting your fish campaign.
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