which Qt is for me?
There is only one Qt :-)
PyQt is a Python binding for Qt and still requires Qt libraries (binaries). So, even if you use PyQt you will need to have Qt libraries which you are using.
If I understood you correctly you need your UI on a computer (not Pi), right? This part is simple - just install the latest stable Qt version an start coding :-)
For the other part you can either directly develop on Pi (using Raspbian you can easily install Qt with apt) or you have to cross compile Qt to develop on your PC. You don't have to cross compile everything, just what you need. See https://wiki.qt.io/Raspberry_Pi_Beginners_Guide