Brig snails coming soon - question

I would treat them just like fish. An airstone and a few handfuls of gravel from an established tank (for bio-filtration) would be my suggestion.

Snails IME have been fine going through the cycle with no ill effects. I put 4 mystery snails through a cycle with no problems. I also have a 5 gallon tank that is just breeding red ramshorns and I'm not even sure that is cycled. I'm sure by now it is since the food I put in probably creates ammonia eventually but it probably took forever. All those snails look perfectly healthy. I actually went probably a month without changing the water in that 5 gallon and found no dead snails. It's almost a bare bottom so I would have found them.

Most snails are quite resistant to ammonia and nitrite. If you have enough of them, they can be used to "fish" (snail? livestock anyway) cycle a tank.

I have taken MTSs and Ramshorns from a tropical planted tank and threw them into a non-planted coldwater tank. They were absolutely fine. I don't know if your Brigs are more sensitive, but IME snails tend to be very sturdy when it comes to water quality.
The only thing I can think of that you may want to worry about is a healthy shell. You will probably want to put some additives in the water such as Kent Marine Concentrated Iodine, Kent Marine Concentrated Calcium, Repti-Cal Calcium Powder for reptiles (¼ teaspoon per 10 gallons), Crushed Egg Shells, Cuttlebone (crushed or whole), Crushed Coral, Aragamax sand, Carabsea Bahama Reef Sand, to name a few. (I use coral calcium.)

Just to let you know, a Brigs snail is also known as an Apple Snail, which get to be very large. You may want to get a larger tank or get rid of them and go with a smaller species such as Ramshorn or Japanese Trapdoor. Here is a link for the Brigs Snail (Apple Snail).

how does the addition of that stuff affect fish though?

You don't have to use all of it. I use the crushed coral calcium and my fish are fine. It is basically like taking vitamins.