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Given the order (P,D,Q,s) of a SARIMA model, s is an integer representing the number of periods in a season. Intuitively, I suppose it would be 12 for monthly data and 4 for quarterly data.

But if I have hourly data (for a whole year) and I'm using only a small number of days as training data (say 10 or 14), what is a proper choice for s?

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The choice of periodicity in a ARIMA model is depending on the seasonality in your time-series data. You should plot your time-series and see if you have a "curve"-pattern that occurs regulary.

Example of seasonality in time-series

Based on the "distance" (hours in your data set) you can make a guess what the right choice of periodicity is.

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