Does the type of capacitors matter?
Yes, the type of capacitor can matter.  Different types of capacitor have different properties.

Some of the properties that vary between capacitor types:


Polarised vs unpolarised
Max voltage
Equivalent Series Resistance (ESR)
Lifetime (electrolytics are particularly bad in this case)
Physical size (e.g. a 100,000 uF ceramic capacitor would be HUGE!)
Tolerance of capacitance (again, electrolytics are bad here, often being +/- 20%


In your link, the diagram shows polarised capacitors, which suggests that they weren't intended to be ceramic (which are unpolarised).

Two types of polarised capacitors are aluminum and tantalum electrolytics.  In your case, I'd use tantalum.