it seems like a large electrolyte with a couple of parallel small ceramic capacitors is a common configuration,
What you are mentioning seems to be talking about Filtering and bypass capacitors. The usually larger filtering capacitors exist to remove low-frequency power supply noise, while the smaller valued bypass capacitors exist to remove high-frequency noise and provide a low impedance path for current surges.
To answer your two questions:
what is the proper type of the capacitors for bypassing the power rails?
The most important factor when choosing a capacitor for this purpose would be its frequency response, which is determined by equivalent series resistance (ESR) and equivalent series inductance (ESL) of the capacitor, as these will affect the capacitors performance in filtering and bypassing noise. In general, monolithic and ceramic type capacitors are used, as they have both low ESR and ESL.
How to decide the number and values of capacitors to put in parallel?
In general, when filtering and bypassing power supply signals, capacitors of multiple values are used to target different noise frequencies. This might include using 3 or more capacitors, one for low frequency noise (large capacitance value), one for mid frequency noise, and one for high frequency noise (low capacitance value). More capacitors may be used to target a wider noise bandwidth. To calculate the capacitor value needed for a specific frequency, I will reference a Texas Instruments application report reproduced below:
For further reading, I suggest exploring the application report as that gives example calculations and goes in depth about uses cases and other filtering methods.