Imagine that you are young Ned Stark at the end of the Robelion. You go back to Winterfell, deeply sad because of the deaths of your father, your sister and your brother. You believe that nobody would have done that to your family if the North would be the strongest kingdom, so you want to improve the North economically and military.
The situation for the young Lord of Winterfell at the begining of the mandate is very good: your vassals are so loyal, the King is your best friend and the Hand a man who is like a father to you and a long summer is beginning. What would yo do?
This is my choice:
-Ask for the iron throne to coin silver money in the Old Mint of White Harbour. This would give the North a good financial position.
-Start serious trade with Braavos. The North have a lot of wood, wool and furs, three things braavosis can buy.
- Start building three fleats: The Merchant fleet, The Fishing fleet and the War fleet. The Merchant fleet for trade with Braavos, Pentos, King´s Landing,... the fishing fleet for whaling, tunas, codd,... the benefits of these two fleets would finance the War fleet. Plus the War fleet would patrol the coasts and make the sea safer for fishing and trading, in a symbiotic relationship. And in winter, a lot of young people can join the fleets and avoid the hard weather.
- Create an important port town in the West Coast. Probably in the end of the river that connects the lake of Torrhen Square with the coast.
-Create two good roads, as good as the kings road. One to connect Winterfell and White Harbour (the capital and the biggest city), the other to connect Barrowton to White Harbour (the two biggest cities).
- Become Winter Town in a proper city. Pave the streets, build a wall, and build some important things like: craftman´s school, a cristal factory, a bank (The Ice Bank),...
-Rebuild the abandoned buildings in Winterfell and give them some use. For example: the First Keep into a militar academy where the best soldiers and commanders of the north will be educated and trained.
- Rebuild Moat Cailing and put there a permanent garrison. It Does not need to be very large: I think a dozen soldier per tower (three dozens total) would be enough for peacetime.
-Train young people in the Militar Academy (the Old Keep). The sons of low nobility could be trained there to be great commanders, promising strong and brave young commonfolks to be good warriors, the elite of the infantry.
-Create a company of 1 or 2 thousand men as a standing army. I would take the name of the badass Ruddy The Ruin and name them the Winter Wolves. People trained in the Academy would form this company, commonfolks and low nobility, very loyal to the Starks. No need to be very large: about 400-500 cavalry, same number of archers, and one or two thousand heavy infantry like roman legionaries. In peacetime, they would train and they would patrol the roads, in wartime, they would be the heart of the Stark army.
-The best warriors of the Academy would form The Guards Of Winterfell: a elite group of 300 strong and skilled soldiers to be the garrison of the castle.
Sorry for my poor english, I´m not native and this is the level I reached in the school when I was young.