Best way to convert Real data into complex data type

[Karn3003]

Best way to convert Real data into complex data type

[NEGU93]

It is likely that if your data is already real-valued, you are good to go with real-valued (conventional) algorithms, no need to convert them just to make it complex.
If you want to convert your real data to complex anyway, you can indeed try something as the Hilbert transform. Or something that makes physical sense, like if you have a time-series signal, making the Fourier transform.

On the contrary, many papers I've seen, that convert complex values to real, use the absolute value of the complex data, ignoring the phase. Or, I would advice if you can, if you have a ND matrix of complex data, transform to (2*N)D matrix with real and imaginary part.

But this is more liked with your application in particular. I cannot do better here than the experts on the topic.