Which connection do I need to operate the projector at full resolution?

Unfortunately I come to an end here with my knowledge and do not have the time to do more research now. It would be great if someone had an answer ready.

It's about our projector.

Resolution: WXGA (16: 9; 1366x800)
Connections:
Composite (RCA), S-Video, VGA In (Dsub-15pin), VGA In (Dsub-15pin), Audio Out (Mini Jack), Network (RJ-45), RS232 (DB-9pin)

But now the maximum resolution of VGA is 800x600. At the moment we're also operating it with VGA, which looks really fuzzy and of course is far from exhausting what it can do.

Now we're converting a little and also need a new cable. So it makes sense that we're now using the right type of connection. I have never had anything to do with the other ports, so I'm unfortunately at the end of it and don't know how to connect it to run it with WXGA.

The connection to the computer should be made via a common connection (e.g. HDMI) because the laptops change more often and we need maximum flexibility.

Simply use a very high quality cable which is also a bit expensive. The same applies if adapters are used. Location cables are also unsuitable. The best thing would be a Wi-Fi connection.

Thank you! So really only the build quality influences the maximum resolution? Well, analog stop.