As climate modellers prepare their code for kilometre-scale global simulations, the computationally demanding radiative transfer parameterization is a prime candidate for machine learning (ML) emulation. Because of the computational demands, many weather centres use a reduced spatial grid and reduced temporal frequency for radiative transfer calculations in their forecast models. This strategy is known to affect forecast quality, which further motivates the use of ML-based radiative transfer parameterizations. This paper contributes to the discussion on how to incorporate physical constraints into an ML-based radiative parameterization, and how different neural network (NN) designs and output normalisation affect prediction performance. A random forest (RF) is used as a baseline method, with the European Centre for Medium-Range Weather Forecasts (ECMWF) model ecRad, the operational radiation scheme in the Icosahedral Nonhydrostatic Weather and Climate Model (ICON), used for training. Surprisingly, the RF is not affected by the top-of-atmosphere (TOA) bias found in all NNs tested (e.g., MLP, CNN, UNet, RNN) in this and previously published studies. At lower atmospheric levels, the RF is able to compete with all NNs tested, but its memory requirements quickly become prohibitive. For a fixed memory size, most NNs outperform the RF except at TOA. For the best emulator, we use a recurrent neural network architecture which closely imitates the physical process it emulates. We additionally normalize the shortwave and longwave fluxes to reduce their dependence from the solar angle and surface temperature respectively. Finally, we train the model with an additional heating rates penalty in the loss function.