If you're new a good starting point is Andrew Estermont in kingsmen.
Drawing ours is the fury every time you attack, and andrew always counting as controlling all the required zones is quite powerful, meaning you'll always be hitting hard.
Next up i think is light bringers with bronn attachment. Being able to shoot off multiple tactic board zones with them is powerful. They are one of the best if not the best ranged unit, as that bonus damage to nearby units helps soften the enemy line up before you charge.
Queens men are a solid unit for holding objectives. with both them and kinsmen sharing to the last and being your hammer and anvil id look at keeping them alive for as longs as possible. For this i recommend tycho and davos unit attachment. dropping down to 1 wound then healing back up to 10 models (1+5+4) is kinda crazy mid game.
Wardens are a good home for davos. And finally id spend my final points on baelish or alester florent as a 2nd NCU. Being able to deny zones your opponent wants is powerful, Lannister's generally rely quite heavily on crowns for both tactics cards, units and attachments, swords and horse for targs and starks etc etc. Also baelish lets you perform the attack at least 3 times in a round trick with your light bringers by going to a zone that isn't bags or swords at the start.
Add a Dragonstone noble or 3rd ncu as preference.
Other combos are:
Mel + Jaqen to copy here abelites in a queens men/faithful army best led by Stannis (one true king) given he heals when the units passes morale tests that mel/jaqen is giving them mitigating some of the damage.
Running zorse riders into someone flank with an attached Dragonstone noble for a serious threat from sentinel can be quite intimidating to armies that dont have cavalry of their own.
Stannis (rightful heir) is any army that can give out a lot of tokens and his best card harsh conditions can be used to turn off for the round some of the hard hitting units such as lance cavalry , (gregor in knights), jon in ranger hunters, greyworm unsullied etc etc