Which Wi-Fi system would you recommend?

The biggest question is would it be worth it for us to buy a professional system like Unifi/Omada or would the home user standard like AVM be sufficient?

As a friend of mine likes to answer in her lectures: "It depends!"

The question is also what one hopes for from the "professional system" and what the fun costs.

which WiFi system would you recommend to me?

WiFi 6.

Everything else is hardware and has nothing to do with the WiFi system.
And the hardware is almost irrelevant – whether Fritz or Ubiquiti or other "brands". They do what you want in the private sector, and for different applications/mounting locations there are appropriate APs.

The data throughput from your provider will not be reached via WLan anyway. The easiest and for the private sector AVM is completely sufficient. I also have a 7590 and 2 7490 as repeaters here and a repeater in the garage, that is enough to get about 200 Mbit data throughput at best.

That may be the case for you, but a modern WiFi system can very well utilize a 500 Mbps connection… However, the client must also be capable of it. The more devices connected to an access point, the slower it becomes because a lot of airtime is used for management. There are already numerous posts on this topic. Having an access point in a cabinet or behind something is the worst idea. For people who are not a bit deeper into the subject (and don’t have the basics down), a system from AVM makes more sense.

I pull 500 Mbit/s here with a standard AVM router over Wi-Fi. That works. I wouldn't know what else I could optimize and where. As a standard user, I am not missing anything ...