It might be more convenient to book in advance, especially as you're only going to be in Amsterdam for a day. But I wouldn't of thought you'd see any difference in price by booking in advance, I could be wrong though.
Yes you are much better buying a ticket online in advance. The train you want is the Thalys. This is the only high speed connection between Amsterdan & Paris. If you book in advance then you can get the best fares. Lowest fares are released 12 weeks in advance and go quickly so check on www.thalys.com or www.nshispeed.nl
If you wait until the day before only the most expensive fares will be available (just like on airlines)
travel on 13/11 €25 one way
travel on 31/08 €55 one way
It's always best to book early.
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