You say you have managed to make your data stationary, so I would probably say an additive model is your best starting point. You could simply plot your stationary data and check that the variance doesn't increase with the nominal values. High variance will mean higher errors for a linear regression.
When we have a basic regression model, like the following:
y = \beta_1x_1 + \beta_2x_2 + \epsilon
the residual error $\epsilon$ is hypothesized to be constant (assuming the model itself is accurate). $\epsilon$ should not get larger when there are larger values for the covariates $x_1$ $x_2$. In other words, you expect homoscedasticity: that the error term is the same across all values of the model covariates. This is what you will easily spot on the plot of your processed (stationary) data.
If you made you time series stationary by taking the logarithms (a.k.a differencing), then an additive model of the
log-ed variables would almost correspond to a multiplicative model.
Just to be clear, if you still seem to have heteroscedasticity with $\epsilon$ varying greatly, this might imply that your model itself is ill-formed e.g. that an important factor is missing.