What, generally, happens to card prices when a new set is released?
There is no way to accurately predict at what price a given card will settle during a Standard season. Pre-order prices generally spike for mythics and obviously good cards, but as the season continues, prices will fluctuate based on what decks make it in the meta.

Worse, some cards in Standard may find a home in Modern, Legacy, or Vintage (or Commander!), which alters the price in an even more unpredictable way given the larger card pool; at least in Standard you can fairly easily look at what combinations you've got available to you, with under 1000 distinct cards.

Judging what cards are low and will go higher, and what cards are high and will go lower, is a process called speculation. Speculation is not an easy thing to be good at, and there are people who make their (shaky) careers on it.