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Experienced in signal/image analysis, and new to data science, I recently was challenged with a relatively simple dataset: 100 to 200 items, about 10-20 numerical variables (in the [0-1] or percentage range), with only one variable used at present time for ranking, and 5 to 10 categorical variables, each with few options. A categorical variable takes about 2 to 4 different values.

I would like first to get insight on potential structures in such data. I have browsed Agresti's Analysis of Ordinal Categorical Data, some have advised me to invest on TDA (Topological data Analysis). Yet I do not know where to start from.

Do you have guidelines, best practices on such REAL data to gradually address the aforementioned issues, from visualization to genuine processing/inference?

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You can get a reasonably good approximation of steps for exploratory data analysis (EDA) by reviewing the EDA section of the NIST Engineering Statistics Handbook. Additionally, you might find helpful parts of my related answer here on Data Science SE.

Methods, related to EDA, are too diverse that it is not feasible to discuss them in a single answer. I will just mention several approaches. If you are interested in applying classification to your data set, you might find information, mentioned in my other answer helpful. In order to detect structures in a data set, you can try to apply principal component analysis (PCA). If, on the other hand, you are interested in exploring latent structures in data, consider using exploratory factor analysis (EFA).

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