My favorite deck so far: [Fire]/Fire/Fire. Aggressive tempo, versatile control, and easy card advantage.
Fire Arrow kills every hero level 4 and below, every T1 unit that isn't Ardra's Boulder, Gilded Glaxx, or an inactive Gargoyle, and a good chunk of building cards. A single Lobber brings the rest of the building cards into range; a Firebat lets you snipe squad leaders and tech buildings.
Doubleshot Archer is nearly always a 2-for-1 if she gets to attack. If you can't keep a unit around long enough to attack, pay 1 more gold for Flametongue Barnstomper Bamstamper Lizzo and pick off a unit now, then make them attack into a 5/x before getting to your other units.
If they build defensively, it's not too hard to find an opening for Double Hotter Fire; just having a Careless Musketeer, charged Bloodburn, or midband Jaina on board gives you 3-6 targeted damage towards killing whatever would otherwise punish playing 2 non-combatants.
You're vulnerable to things that can snipe Jaina, like another Jaina, Doom Grasp, and certain hasty/evasive units. Very large units make your removal inefficient, so it might be worth swapping the third Fire out for Blood, for Kidnapping and hasty units. (Hasted Lizzo deals 5+3 damage to a patroller, enough to kill even most T3s). Law might be interesting - Bigby draws cards, wipes the board except for spellcasting heroes and Hotter Fire, and preemptively counters tough T2s. Or maybe accept you aren't gonna keep Jaina alive much and go Necromancy for Garth card draw, Blackhand Resurrector, and killing heroes on alternate turns with Fire Arrow and Doom Grasp, freeing Jaina to spend more time burning buildings. (also Bloodburn synergy.)