I think there can be a lot of different kind of lord and ladies, it all really depends on what kind of nobility you want to be, but if I were to rank skills that would be a must, I would rank them as such (only for nobility that wants to be very "active" in the running of their domain):
1 Calligraphy - Writing is important because of contracts, if you want to set up some taxation, having the ability to write those explicit contracts can be important. (Not as much laws and such, since that's more the domain of the king, depending if SBS makes some changes, but we'll see)
2 Document Replication - This all depends on if documents will be worth replicating, but I imagine if you want to write a contract, being able to replicate it can come in handy quite a lot, also if there're laws you want to copy so you have them by hand etc.
3 Misinformation or Inquiry - Depending if Inquiry ties into the gossip system or not, but being able to dismiss gossip and create gossip could be incredibly useful to characters, not just that but being able to trade information that increases or decreases your reputation or the reputation of the nobility around you can, in my eyes, be important.
4 Increasing your own prestige/like-ability. There are a few ways to do this, but it all depends on how you wanna go about this, the few ways I would say is.
Performing arts (dancing) as you can then participate when invited by other nobility, and increase your reputation by your skill in dance, as balls etc. are said to increase your reputation, so I imagine a few lords might want to keep their prestige up by holding a few now and then.
Combat - Surprised, perhaps, but combat is another way to increase your prestige/reputation, it's not necessarily the most peaceful route, but you go it if you want to set yourself apart from others on the battlefield. (Or if you want to take over more land, increasing your power that way.)
Musical Arts and Song - I put this in here as it, like combat, as it will most likely help your reputation/prestige, it can help making npcs etc. like you more.
The last skills would be:
5 Acts of good.
I put acts of good on the last point, this basically encompasses most of the crafting/farming/helping your community. Farming might not give you as much appreciation, but you'll help a little here and there, same with crafting or medicine, closing wounds etc. might help a few people, but we don't really know how much of an impact it will have on your reputation/prestige.
There are a few other honorable mentions I think could come in handy:
Makeup - Important if it can increase your rep/prestige, if it's only used for disguise then it might not be as good.
Camouflage - If you want to disguise yourself during some very specific situations.
Engraving - If engraving your seal/etc. increases your rep/prestige etc.
Waterfinding, Surveying and Horticulture if you're the kind of nobility that wants to work in close relations with your community, in mapping out and making your domain as optimal as possible.