Does it matter what material the flask is made out of? I noticed some are pyrex, some are borosilicilate.
IIRC, Pyrex is simply a particular brand name of borosilicate glassware
Correct. Wikipedia: "Borosilicate glass is sold under such trade names as Kimax, Pyrex, Endural, Schott, or Refmex."
It really depends on your process. If you want to make the starter, cool and then transfer to the flask, any lab flask will do and you save some $. If you want to be able to boil and cool in the same flask, then you need some form of borosilicate glass.
The sticking point on this is your stove. If you have electric coils, don't bother. It will crack. I have a glass top electric which distributes the heat well. So far I've had no issues......fingers crossed. If gas you should have no fear of cracking on the stove with Borosilicate.