With your 3 card, similarly to 4 card, you are usually trying to win the battle and do damage. Having that in mind:
1. Ser Loras Tyrell - many a Tyrell victory came thanks to Loras giving Tyrell additional attack before rest of the houses have chance to plan and put into motion a counter
2. Ser Gregor Clegane - 3 sword icons is the most direct damage you can do in the game and since you are looking to win battles with 3 card, damage is what you are going for. Only Blackfish can thwart him
3. Victarion Greyjoy - allows GJ to dominate the seas, which is crucial strategically
4. Renly Baratheon - his skill doesn't help you win the battle, but if you do win, ability to upgrade a footman to a knight is nothing to sneer at
5. Rob Stark - some will probably not agree with this low ranking, but while in theory being able to dictate where defeated enemy retreats could be huge, I haven't seen it make major difference too often, probably because north is relatively crammed and there are not many options to choose from
6. Areo Hotah - as already noted, with 3 card, you are looking to win, fortification can be useful if you miscalculate, but if you're playing well, it shouldn't come into play too often