Uesugi starts off in the northeastern corner of Japan with what looks like the largest stretch of land out of all the clans. Their backs are against the coast, which is a great defensive position.
Koku is also not a problem to start with as Uesugi lands are among the best farming lands in the country. Not to mention they sport a nice gold mine in Dewa, which starts off completely isolated from enemies, and a silver mine in Echigo which is a river town and easily defensible.
A hidden treasure that most will overlook is the island of Sado. It has iron and sand deposits which allow for the building of an armory. It is only bordered by Noto, which is a rebel held province with little ambition to expand into Sado in the early running.
To bolster their army Uesugi get samurai archers for cheaper than the other clans. The archer is no slouch on the battlefield. In one battle I had a unit of 50 archers, which held a hilltop and took well over 250 heads while only loosing 3. Now who wouldn't want them on the battlefield?
Now the one and only downfall I see with this clan is its starting land is so vast they do not have a big enough army to defend it at first. Hida and Shinano have Hojo, Takeda, Imagawa, Oda, and rebel states bordering it. Shinano alone has 9 borders to defend. With that kind of land to defend it would seem the Uesugi would spend most of the game defending the territory and building an army every turn they have. However, this need not be the case.
First things first, take care of the negatives that face the Clan. Hida is an outlying territory for Uesugi and contributes only 120 Koku a season. 120 is not worth spreading your forces thin enough to save Hida. Shinano on the other hand produces 340 Koku and gets a +1 honor bonus to Cavalry units built there. However, it does have 9 borders to defend against 4 enemies, most of which you don't even need to be fighting now. So, I let Hida and Shinano go, abandoned them completely. This left me with 1580 Koku per year and a silver and gold mine bringing the total Koku to 2580! And the threat of having 4 different clans attacking your initial small army has now vanished. You have two real borders to defend, Mutsu and Echigo. Remember, Sado has very un-ambitious rebels on its border so only a few units will be needed to keep them at bay in the beginning. Echigo is a river territory so taking it from you will require a big army so that is a plus now.
The underlying bonus that I did not mention is that with only 2 borders to defend, Clan Uesugi has freed up resources to develop technology and with their Koku income they can do it VERY quickly. What to build with all the money? With out a doubt you will need to build those mines in Dewa and Echigo. 1000 Koku is a lot of money in Japan at his time. Just to compare, Clan Mori's entire starting Koku is a little over 1100.
Get a castle up in Sado and build an armory and a spear dojo. You can do these right in a row just put them in the job queue. Once they are done you need a large castle and a famous spear dojo. At this point you will be able to build naginata. The naginata in my opinion are the best troop for this clan next to archers. They can hold a bridge for what seems like forever while your army of archers rains arrows on the enemy. The naginata will suffer very few casualties even though you are shooting right into there melee.
During these years however you need to produce Yari samurai and Archers in Mutsu to bolster your defenses in Echigo and especially Mutsu. In a few short years Hojo may start attacking Mutsu. Probably because of the pressure he is receiving from Takeda in the southwest.
After the mines are built and you are producing naginata out of Sado you now have a clear picture of what you should build where. In Sado I produced yari Samurai and naginata, while in Mutsu I produced Archers.
From here start building up the structures in Mutsu. Get your castle up because that holds the key to the rest of your buildings. I built my special unit buildings next, Tea House and Ninja House. By producing a ninja early I was able to kill lots of low-level emissaries and get a high honor level for my ninja early on. By getting the Ninja honor level up you have the ability to start assassinating generals, generals leads to higher level generals, higher level generals lead to daimyo heirs. Being able to assassinate any of these people will make the game much easier. The shinobi were in valuable as my spies in Hojo territory. I always knew what he had in the surrounding provinces and what he was coming with when he was about to attack.
At this point you can sit and wait while your army gets big and your enemies start killing each other, your ninja can always help in that role J. Offensively speaking you don't have a lot, if you chose at this point you can build a Buddhist temple and start producing a few monk units. Or if you have the legendary swordsman event then you can build a sword dojo. When you start your expansion crusade you will need a few of these offensive units. Monks are the better choice than No-Dachi, however they are more expensive to get, but that may not be an issue with the income you will have from your improved farmlands and mines.
Where do I go now?
By now your army is huge and your probably running out of money to even support them so its time to expand. Where to? This is a no brainer - Hitachi! It is a 640 Koku territory and if your lucky by this time Hojo will be actively fighting everyone on his western front so coming in the back door should prove easier.
Once you have taken Hitachi you have another territory with iron and sand deposits. Build an armory and a horse dojo and a spear dojo. This is going to be your cavalry producing territory. Now you have all the unit types being produced in your army. But now you are starting to expand and Sao is looking farther and farther away. Have no fear, build ports. One in Mutsu and Sado. This will allow you to move troops between your two main troop facilities in one turn. Instead of the 4 urns it would take from Sado to Hitachi.
The next target is Shimotzuke. It has a terrible Koku yield of 210 in comparison to the other Hojo lands and your own for that matter but it does have a copper mine. Should be the same fight in Shimotzuke as in Hitachi on the same terrain. This leaves you with only one territory on your capital's border and that's Kozuke. Take it. If Oda or Takeda or Imagawa have become a major power to the west of Hojo, he will be all but extinct. If Hojo has become the power moving west then most of his troops are over there fighting off the remainder of the Oda or Imagawa or Takeda or maybe even the Mori, but either way he is fighting over there.
At this point the expansion dreams are up to you. The situation around you at this point may be different than what it was for me so it's hard to say what to do next. Keep these points in mind.