The stats are here (Rank 3 to Legend). I did not include Legend Rank games because once in low legend, most opponents are playing off-meta decks. If you seek to climb to Legend using a fun but competitive off-meta deck, look no further.
First, this is a mid-range deck in terms of pace! This means that some opponents are going to be faster than us in establishing board, while against slower opponents we will have be the aggressor. Having different game plans against different decks are part of what makes this fun. I can see that many people may treat this as a control/slow combo deck when piloting it because the deck contains good anti-aggro tools and Rexxar. But no, in the wild Wild, Rexxar itself is far from enough to give this deck a decent late-game (especially against Big Priest), but he helps a lot against other mid-range decks (particularly Even Shaman).
Common decks that are faster than us include: Odd Paladin, Odd Rogue, Murloc Shaman, Aggro Paladin, Mech Hunter, Aggro Secret Mage, Aggro Druid, Pirate Warrior. Against those decks, our game plan is to clear their stuffs early on and once you gain board control, go face to apply pressure. We have no healing except one Zilliax and possible Zombeast from Rexxar, so don't give them too much breath room.
Common decks whose pace is similar to us include: Even Shaman, Even Warlock, Cube Warlock. Against them we need to maximize tempo: whatever produces most board advantage for you is often the best play. If you don't have Rexxar in hand, push face damage mid-game and force opponent to trade is very important, so that your hero power becomes a constant threat.
Common decks that are slower than us include: Big Priest, Cyclone Quest Mage, Jade/Maly/Togwaggle Druid (they use the same defensive core), Odd Warrior, SNIP-SNAP Warlock, Reno Warlock, Treachery Warlock (quite common in CN). Maximize tempo in the early game to create a complex board with some deathrattles, but once you have the board, don't spend all your resources just to make it bigger (even Cyclone Quest Mage which doesn't run AoEs may have Frost Nova + Giant). Try to play around their board clears if possible (e.g., Defile, Mass Hysteria, Poison Seeds, Spreading Plague, Supercollider).
Always keep: Nerubian Egg. Yes, this egg is the most important card for this deck. Turn 2 Nerubian Egg + Turn 3 Terrorscale Stalker is great opener for any matchup. So if you have Nerubian Egg, keep Terrorscale Stalker as well.
Keep against Shaman, Druid, Warlock and Warrior: Deathstalker Rexxar. I have to emphasize, again, don't rely on Zombeast to play late game against Big Priest. Just don't.
I generally don't keep other cards unless I have some of the above mentioned cards. The exact judgment in mulligan requires practice, and exceptions exist. But when in doubt, follow the above rules.
Kathrena Winterwisp: it's harder to replace because of her Witchwood Grizzly and Charged Devilsaur synergy. If you don't have her, I'd recommend taking out the two Grizzlies and the Charged Devilsaur as well, and add in two Secret Plans, one Wandering Monster and a Zul'jin (which hopefully you have or are more willing to craft).
Zilliax: if you haven't crafted Zilliax, do so. It's perhaps the most used card in hearthstone history. Plus, Zilliax onto Explosive Sheep is just sick. However, if you're absolutely low on dust, try a second Unleash the Hounds.
Happy climbing and let me know in the comment if you have any questions or constructive suggestions!