Selection of substrate is based on the material to be deposited and also for what purpose the film is being deposited. The most important criteria is adhesive property. If electrical properties are to be investigated, substrates should be highly insulating. No barrier should be formed at the interface. For optical studies, substrates should be transparent in the wavelength range of measurements.  Substrate temperature is found to affect structural properties of thin films. Substrate cleaning is also important for good adhesion.For electrolytic deposition, metallic substrate may be chosen. Thickness range is also important for the selection of substrate. Selection should be such that electrical, optical and structural properties should not depend on the substrate.

Selection of substrate is based on the material to be deposited and also for what purpose the film is being deposited. The most important criteria is adhesive property. If electrical properties are to be investigated, substrates should be highly insulating. No barrier should be formed at the interface. For optical studies, substrates should be transparent in the wavelength range of measurements.  Substrate temperature is found to affect structural properties of thin films. Substrate cleaning is also important for good adhesion.For electrolytic deposition, metallic substrate may be chosen. Thickness range is also important for the selection of substrate. Selection should be such that electrical, optical and structural properties should not depend on the substrate.

When deposition of thin film on different substrates it should be bear in mind the mismatch in coefficient of thermal expansion between the substrate and the thin Film. High mismatch may lead to coating failure by delamination. However, if the thin film has low yield strength it may relive the induced stresses and can substitute for the large mismatch in coefficient of thermal expansion between it and the substrate.

You should specify your question more precisely. Are You asking for parameters of thin films (i.e. properties of thin films) or process parameters? If You are asking for thin film properties (which looks more probable), then:

The question is more complex than it looks like in my opinion. The crucial aspects (in general meaning) are at least interface enthalpies and surface morphology/structure of substrate.

Interphase enthalpies determines growth modes of thin films – i.e. island growth mode or layer by layer growth mode (or transient growth mode) which led to totally different ”films” especially for low thicknesses.

Surface morphology/structure of substrate become important especially for higher temperatures where the surface morphology is important for heterogeneous nucleation (and subsequently crystal growth) or for growth of some oriented structures. Structure (long range order) of substrate may moreover influences crystal orientation of thin film or even identity of crystalline thin film phase due to epitaxial effects.

Some specific issues are involved as well – e.g. possibility of reaction (or creation of solid solution) between substrate and thin film, influence of crystallographic parameters of substrate for (homo/hetero)epitaxial growths, influence of substrate conductivity for plasma-based growths (e.g. DC sputtering), influence of thermal conductivity of substrate for high temperature load deposition techniques (e.g. thermal evaporation), etc.

And, as mentioned above by others, some parameters are important for practical utilization of thin films, like adhesion or delamination due to different thermal expansion coefficients.

Generally properties of thin film resulting from its composition and structure (and thickness, if the quantum effects take place). Thus only change between amorphous and crystalline nature of thin film causes change of (nearly) all properties – physico-chemical, mechanical, optical, electric, ... Moreover, crystals are usually anizotropic...

There has been quite a complete set of  answers to your question. In my opinion, you should first consider the technique whether Physical or Chemical (Pulsed laser abaltion, sol gel, plamsa RF, Sintering, ...) that will be used for deposition; then the type and properties of the material that will de deposited ( metallic, insulator, a ceramic, polymer mixed from two sources etc..) and finally the thermodynamic conditions, especially temperature and pressure. plus the Kinetics, rate of deposition, rate of cooling after deposition  etc...

This will help in determining the type of substrate to be used, the optimum substrate temperature and depositons parameters to be used.

So the question is more complex than it seems.