So a bit late here, but why not add my two cents?
So Tully Commander, purposes of synergy I'd roll with Brynden Tully 'The Blackfish': reasoning is that his Commander cards, unlike his mounted varient, tend to work rather universally, with just ruder benefits to Tully units.
As far as NCU's go, regaurdless of how you build your force there are three I HIGHLY recommend having at least one of, they are Eddard Stark, Catelyn Stark, and Rodrik Cassel. If you not sure who to use for your list and you wanna play with t, just take Eddard of these three and be a jerk at least 3 times.
Now for units, and hear me on this Imma list some recommendations that are not Umbers. Noone needs another paragraph about the greatness of Umbers.
For consideration...
House Bolton Cutthroats: I know right? Wierd. I actually prefer to put the Blackfish in this unit !yself, it's cheap but decent, the greatest weaknesses of this are it's armour value and moral. Stalwart benefits by turning this from a 7+ to a 5+, which is kinda dumbwhen paired with "Blackfish's Resolve" or the "Refuse To Yield" tactics card, also cute on both ends when Eddard is an NCU.
House Tully Sworn Shields: No duh, I have three recommendations for this unit, though do what is comfy for you. Firstly, Sworn Sword Captains, the largest drawback to Sworn Shields is their lack of penetration. 7 dice on 3+ is mighty fine but most fielded units are kind of a pain. Sword Captains however have "Order: Martial Training" which after your attack dice are rolled, gives the opposing unit a Vulnerable Token, which is nice. Pair that with some tactics cards foor either offense or defence (such as Set For Charge or Winter is Coming" and it's surprising how much damage the little tanks that could are capable of. My second recommendation is the painfully expensive Greatjon Umber. He makes the unit a painful 10 points but for the added bonus of a free charge from the tactics board, a Stark classic, and rolls of a 6 don't allow saves. The choice is yours there, I highly recommend the Captains, but Greatjon works great with Eddard or Rodrik in this regard. The third one is Meera Reed. I listed her last because she is a bit tricky. For defensive play she is damn good for 1 point but other than that you can accomplish greater things with the other two, but don't discount her, a possible 3 free wounds and a disorders charge into a shield wall or set for charge is just gross. A fourth choice is Syrio Forel, simply makes this unit rude at least once a turn.
Stark Sworn Swords: these are always great, pair them with Tully is you want to love and hate yourself, or with Maege Mormont or Brienne for a suicide torpedo (very likely to die but all but garunteed to kill whatever you run them into), highly recommended you take Eddard or Catelyn for this unit.
Stark Bowmen: their praises have been sung above by Oakwolf, and the combo when they have a Crannogman Warden with them is just ruder. What's also rude is if Rodrik is your Commander and he is in this unit as his "Press the Advantage" gives the unit critical blows on a 5+, but I'm crazy so yeah. I wouldn't really recommend these guys though, are they great? Yes. Is the Shield wall combo agrivating as hell? Yes. But they tend to be the easy target of moral based attacks, and it's kind of a shame to waste Brienne or Maege on them.
Crannogman Trackers: same as with Bowmen, but shorter range and more synergy with other units.
Bolton Bastard's Girls: same as Crannogman, but with strangely better synergy, though better with a different Commander. Still, all three ranged units should be considered.
Stark Outriders and Bolton Flayed Men: these are great but I just don't recommend them for Tully, even the mounted one...not as a Commander mind you. Flayed Men are devastating with the Commander attachment, but I personally find the non-commander mounted Tully to be best used in the Outriders. Hear me out: for Flayed Men, the Commander varient increases their movement to 6, which makes the average, however the sheer brutality of the War Flail(critical blows and vicious) when paired with 'Ride Them Down' and/or 'Heavy Impact' tactics cards is just...just rude. 'Ride-by Attack' works better with the Outriders, because 14 inch movement is dumb. Now, the reason I prefer attachment Tully to Commander in the Outriders is because of 'Regroup'. Outriders charge, smash, they get hit? Order: Swift Retreat, Regroup, heal d3+1 wounds. Tadah. Work stupid well with Eddard, Rodrik, or Robb as commanders.
That...should about cover it for units...umm NCU's...
Sansa Stark: always useful, even in a bind. Tactics cards are important.
Catelyn Stark: again, always useful.
Eddard Stark: great synergy with Blackfish on defense and offense.
Rodrik Cassel: great synergy with any list trying to focus on more agressive tactics. Works great with Greatjon (I did that on purpose).
Arya Stark: functions both similarly and differently than Sansa, still useful, especially in objective games. Get the Shields into the fight.
Petyr Baelish and Lord Varys: these two are useful in nearly every force but are usually not needed as you have better options.
So yeah...that my two cents. I hope it proves at least somewhat informative. Oh! A side note as to why I left out the Umbers.
Umber Units are damn good, but I've been playing Starks since the game released and frankly...that is all I see. Lannisters? Either Tyrion, Tywin, or the Mountain, maybe a High Sparrow or Joffry. Bolton are either neutrals or mixed with Lannisters of Nightswatch. Nightswatch and Freefolk are...themselves, but Starks...might as well call the faction Umbers. So I've actively tried to make other units and commanders more competitive through combinations just to break up the monotony. And before anyone comments on my listing of Greatjon Umber, the attachment doesn't count as an Umber nor make the unit an Umber, only the Commander...so in the thinnest of technicalitys I've stayed true to that.