Which train (there seems to be so many different ones...) would I need to take to Brugge from Paris? and from Brugge to Amsterdam (Haarlem)?
The quickest way to get to Brugge from Paris is to take the Thalys line from Gare du Nord to Brussel Zuid, then hop on a Belgian rail (NMBS) train to Brugge. Trains leave hourly from Paris, and there's at least two per hour from Brussel Zuid in the direction of Brugge. One ticket covers both legs of the trip. There's also a cheaper option on French rail with an extra train change at Lille, but I don't know too much about this.
From Brugge to Amsterdam (not certain about Haarlem), take NMBS to Antwerpen. From there, you can take Thalys (more expensive but not much faster) or an ICE train to Amsterdam. Once again, one ticket covers both legs of the trip.
Here's the relevant websites:
http://www.thalys.com/nl/en/?time=1269382237
http://www.sncf.com/fr_FR/flash/
You may be able to get some discounts by booking in advanced, but otherwise, you can just as easily buy your tickets on the day you travel.