I think the normal ninja v is good enough for the a7iii.

If you want to record 4k 120fps with another camera in the future, you'll need the v+.

But for those rare cases you can also record to the SD card. So the basic version is usually enough.

On the Atomos website (https://www.atomos.com/products) you can view the products sorted by your camera. Many models are compatible.