The choice of which molecule to keep constant and which to vary will depend on the experiment type, the properties of the molecules and the stoichiometry of the interaction.
For ITC, where neither protein is labeled or immobilized, either molecule can be in the cell or syringe. You will need a higher concentration and total amount of the molecule in the syringe, so solubility and availability will generally be deciding factors. For protein/small molecule interactions, it is most common to put the protein in the cell and the compound in the syringe.
The amount (volume and concentration) of sample that you need will vary by method and by the Kd (equilibrium dissociation constant) of the interaction. For guidelines see the CMI technology comparison table. Binding assays will typically have one binding partner at a fixed concentration (or immobilized on a surface) and one binding partner at a variable concentration. The high concentration for the variable analyte will typically be 10-100X Kd,... Read more about How much sample is needed for a binding assay?
