If you simply want to understand a film as best you can first consider the type of material and range of properties you expect (eg is it organic or inorganic? metallic, semiconductor, insulator? soft or hard?) This should narrow down to a set of applicable techniques (all the "allowed" techniques) and allow you to find what people most often do to understand these films. After this consider what particular properties you need to answer the questions you have about the film. The opposite holds if you want a particular property measurement: You already have your question and know what information you want so then you only consider the limitations of each technique and choose based on the type of film.
Eg if you have a new type of photoresist you are developing you know you have a polymeric film (probably insulating, although not necessarily, most often weaker than metallic films. Prone to alteration by light, etc). So you have to choose techniques applicable to the film. If it's truly homogeneous and on a simple substrate that allows you to maybe perform the following possible techniques: ellipsometry, ATR-FTIR, xray scattering, TGA/DSC, van-der-Pauw resistivity. But you still would need to look at what questions you want to answer and what could go wrong: does it matter whether you know the resistivity? Would you have any reason to observe diffraction peaks or any reason to care? What diffraction peaks would you see (eg chain alignment is ~ Q ~ 15 /nm, but crystal supercells can be Q ~ 2 /nm). If you're doing spectroscopy how do you know you're not changing/reacting the film further over the course of the measurement. (There are literally thousands of papers in each field dedicated to this so look at lit reviews on the material)
Very general question. So the answer is... well, it depends.
The characterization techniques you need, should have in consideration:
1) the thin film it self and the substrat: material, thickness, electric proprieties, optical proprieties, physical proprieties...
2) minimum characterization necessary to validate the success of making the film
3) desired information / characterization desired to know about the film
4) techniques you have access (directly or through others persons) and the ones you are capable of extract results.
A very simple example: deposition of a thin film of crystalline silicon glass substrate. We need to find techniques capable of providing information about the crystal structure.
In 1) we know Silicon is a semiconductor, not a good electric conductor and not transparent at visible light. Glass is an insulator, and transparent.
In 2) we start by a visual inspection, measurement of the thickness, ...
In 3) techniques to determine crystallinity: X-Ray Diffraction (XRD), High Resolution Transmission Electron Microscopy (HRTEM), Raman, ...
In 4) XRD provides large analysis areas, is cheap and for a single thin film easy to extract results; HRTEM is very expensive and can only provide a analysis of a very small area; Raman can be used for large areas is cheap, is easy to extract results, depends of the optical absorption but is not available. Then the XRD is the best technique available.
Although not necessary for the objectives, other techniques can be used for a better characterization of the sample, for example electric characterization of the silicon layer, roughness, ...