I think anywhere in Sussex is very much horse country-- hard to imagine you would go wrong with any of those hunts, or any hunt in the UK for that matter. Most of them have been around for a very long time, well-established traditions, strict adherence to standards, etc, so unlikely you would run into a dodgy hunt. I don’t hunt in the US and never have in the UK, but do know that in the horse world in the UK, what you wear, sticking to their traditional rules ( which can vary a great deal from that in the US) matters a lot. Whether the rules would be bent somewhat for a guest, I do not know.
I hope you find something-- it sounds very exciting!