Ischia Ponte has a lot of people on holiday and their safety is a matter of image for the whole island. There are plenty of security guards and most beaches have a lifeguard service. The island is small and difficult to get lost on, so you'll get help anyway.
As for your savings, just be careful as guests come in all shapes and sizes. Don't show large sums and don't leave valuables out in the open.
Also remember that Italians are impulsive, sometimes hot-tempered and extremely noisy, so don't argue with them unnecessarily.
It's worth noting that only a small percentage of Italians speak English well, but locals understand sign language very well, so it's possible to find a common language if you want to.
