I would not go straight to a 12ga. Might form bad shooting habits early on due to being too much gun. I grew up on O/U 28 and 20ga. Very easy to operate as you said and even better in your situation with multiple kids that are not all right or left handed. That being said you will probably spend...
I have both the vx5 and the zeiss v4. Both are great, however I prefer the zeiss due to clearer glass and I like the zeiss turret design slightly more.
I am looking to buy a leica binocular neoprene strap. This is the one that comes with the geovids and the ultravids. They might have changed the design recently. I attached a picture of the one like I am looking for. Thanks