MST experiments on the Monolith NT.115 pico require that one of the binding partners is fluorescently labeled.
For protein/protein interactions, start by considering the amounts, solubility and sequence of the proteins. The labeled target is typically used at 5-10 nM concentrations (200 ul/titration). The unlabeled ligand is ideally used at a concentration of 100X Kd (equilibrium dissociation constant), so could be uM to mM for weaker binders (20 ul/titration). If one protein is much more soluble and/or more abundant, that may be a better choice for the unlabeled ligand. If one protein has a convenient labeling tag (such as His-tag or sortase tag).
For protein/small molecule interactions, you will typically label the protein, as labeling of small molecules is often difficult and or disruptive to binding.
Unlike fluorescence polarization, the relative size of the molecules isn't generally the deciding factor when choosing which molecule to label for an MST experiment.