What kind of hard contact lens case does everyone use?

It's been quite a while since I switched to hard lenses because my dryness got so severe after using soft ones. However, since I've only been using the suction cups provided by the optician and the basic hard lens case, I don't know if I'm managing them properly, but I keep getting cloudy foreign particles stuck in them.

Every evening, I apply a dedicated cleaner and scrub them vigorously with my fingers. Since the lenses are so small, I tremble with fear that I might drop them in the sink. More than anything, I get stressed every time I clean them because I'm worried about scratching these expensive lenses. Do you all wash your lenses by hand like this every time before storing them in a hard lens case?

I've seen machines lately that double as hard lens cases and clean using ultrasound. If I use something like that, will I be able to keep my lenses clean without having to scrub them by hand? I'm so sick and tired of my eyes stinging and getting bloodshot by the afternoon. If anyone has used a cleaning machine, please share your honest reviews on whether it's really worth the money! Haha.