So, from what's been said:
- You only get Basic and Classic cards from all classes.
- Basically, cards are put into various categories (Value, Tempo, AoE, Card Draw, etc.) and the effect chooses the most appropriate categories for the current game state, and then you get to choose a good card from one of the categories.
- It's possible that the cards you get are all from the same category, depending on the game state.
- It tries to give you something you can play this turn (with the mana you still have).
- If not possible, it gives you something you can play next turn.
- You don't really get any bad or uninteresting cards.
- Peter Whalen said that you will be offered a Crazed Alchemist if there is a Doomsayer on your opponent's board, so the effect can get very specific in the answers offered.
- Other things you are offered: AoE if your opponent's board is full. Single target removal if your opponent has a large minion.
- The effect seems to be deterministic: With the same board state/mana/hero health, you get the same options. For instance, on turn 2 with no minions on board, you get offered Wild Growth, Animal Companion and Brightwing.
- Mike Donais hints at it offering you Hungry Crab when there's a Murloc on the opponent's board.
- (Pure speculation) Maybe if your opponent is low on health you'll get some direct damage spells? And conversely, you get healing spells when you are close to dying? Edit: This has been confirmed!
Overall, seems like a card you don't really want to play on 2, since it might get much greater value later in the game.