While Priest isn't the strongest class, its always been my favorite.

In the mulligan: Try and get a 2, 3, and 4.

First first part of the quest reward: Look for a 5 or a 6 if you have not drawn them. If there are none, a 7 or an 8 will help the third stage.

Second part of quest reward. Look for a 7 or an 8 if you don't have one in your hand. If you don't need either a Thrive in the Shadows, even a second one, or a Spirit Guide is always a good choice to find the Purified Shard after playing Xyrella, the Sanctified, the quest reward.

Things to remember:

1. Dont play an 8 cost card with Strongman in your deck if you have not played the 7 cost card part of the quest. Playing the 8 before Strongman will corrupt it and it will cost 0.

2. Always make sure you have room in your hand near the end of the game, never play a [Hearthstone Card (Sprint Guide) Not Found] with 8 cards in your hand.

3. Beware of secrets. Counterspell from Mage, and Paladin  [Hearthstone Card (O My Yogg!) Not Found] can ruin your game and leave you without a win condition when playing the  Purified Shard.

Alternate cards:

Shard of the Naaru - Useful against almost any deck. Its also tradable to help find cards you need.

Acidic Swamp Ooze - A second one can help against Warrior early, Shaman, and Warlock.

A second Strongman isn't bad if you don't have Mutanus the Devourer. Mutanus is ok, but its not essential. A 0 cost second Strongman later in the game is quite nice.