Furyblade Vampire vs Blinding Mage
Furyblade Vampire has a triggered ability, and Blinding Mage has an activated ability. In this case, that means that the player with the Vampire has more restricted options, and basically has the worst expected outcomes with this interaction.

Here's how it plays out (let's say Amy controls the Furyblade Vampire, and Nat controls the Blinding Mage):


Amy's Beginning of Combat step starts. Furyblade Vampire's ability triggers and goes on the stack.
Both players have an opportunity to act. Nat can activate Blinding Mage's ability at this time, but he's probably better off waiting.
Furyblade Vampire's ability resolves. At this point, Amy chooses whether to discard a card.
Both players have another opportunity to act. At this point, Nat can choose whether to activate Blinding Mage, depending on whether Amy chose to discard a card.