What it means by first effect is that it won't use any additional effects the card might have, e.g. Dark Bargain will destroy the two random minions (if possible) but will not use the discard effect, and Soulfire will deal 4 damage to a random enemy, but will also not discard anything afterwards.
So, basically you discard two random cards to get one random card of the destroyed minion class. For example, if you destroy a Mal'Ganis you can get a random Warlock card. Or, if you destroy a Sylvanas Windrunner you can get a random "All classes" minion.
P.S.: The card you got from the battlecry will not be discarded!
It is a random druid card/s. Specifically targetted at Mill and Astral Communion Druid.
As usual, the discard mechanic does not apply to cards discarded through Fel Reaver or similar, but only applies to cards lost through effects such as Succubus and Doomguard, and overdrawing.
Despite the wording suggesting you choose one multiple times, it is just one choice for the bunch of them. The first option, to Restore 3 Health is specifically targetted at Mill Druid; allowing it to survive well into fatigue and hopefully win the game. The adding random druid cards is targetted at Astral Communion Druid; letting Malfurion fill his hand up after gaining 10 mana and losing his cards.
Last note, I made it legendary because I think that it could be oppresive, but it is possibly more fitting for an epic slot, seeing as it would be absolutely terrible in arena.