Well I'm part way through a Legendary Uesugi campaign and wow it's living up to it's reputation!! Frist a few random thoughts:
Uesugi have a deceptively bad starting location, it looks promising to the untrained eye, but contains many traps which must be negotiated in order to survive the crushingly brutal early game. So lets start with a few discussion points regarding early expansion and territorial gains:
EXPANSION & SURROUNDING TERRITORIES
1. Yamanouchi - your vassal. Wow great, you start with a vassal, free income, trade, and a nice secure border! ....but no, instead your vassal is basically a hate generation mechanism that will ENSURE you get into early wars you would rather avoid. If it isn't Takeda, it will be Hojo, or later Satake or Satomi, or usually two or three clans at once. They will invade Kozuka and you will have to back your ally or break the alliance and take the diplo/honour hit. Given that war with most of your neighbours seems pre-ordained with when playing Uesugi I backed my vassal, and actually ended up fighting with him and defeating a large number of Satake troops. But each game will be different so play this by ear which brings me to my next point...
2. It is a complete bun-fight on the plains to the South and every game will have a different outcome. Playing Uesugi your fate will hinge on what happens down here and how you play the diplomatic game. There does however appear to be a few very probable events - Takeda will take North Shinano province, then will head either West into Hida or East into your vassal. Hojo will head North, and are inevitably on good terms with Takeda. If Hojo get established, dealing with the Takeda/Hojo alliance is going to prove very difficult. Diplomacy is crucial - try to get Hojo tangled up with Satomi and heading West rather than North. Takeda will have to be dealt with, but if you can take him on without Hojo breathing down your neck at the same time life is easier.
3. Your other neighbours. Part of what makes Uesugi so mental early on is that your home province borders no less than 7 seperate clans. So choosing which way to expand early is crucial. My first attempt at Legendary I happily followed the preordained path to war with Jinbo in the Etchu province. Trouble is that Etchu province is terrible. Meager fertility and borders with 3 additonal clans (one of whom is those Ikki psychopaths) just don't make it a worthwhile investment in my mind as you won't have the cashflow to survive. My second game I went straight for Sado with it's goldmine - this seems a much sounder strategy, and works quite nicely as if Jinbo come after you, the distance to your captial mean they will probably be wiped out by one of their neighborus before their stack even gets to you (which is what happened in my game). The Ashina & Mogami clans to the East are both likely to survive the initial opening salvos and are both freindly towards you so make great buffer states. While Uzen appears an incredibly tempting target I don't think it is feasible to capture this province early on as you will be having a hard enough time just surviving. If you can somehow stabilise your Southern border and feel like taking a risk go for it - but it isn't something I would plan for until much later in the game.
4. Ikko Ikki DLC - if you have pruchased the Ikko Ikki DLC (which you should they add a lot to every campaign) then you have got a potential Tiger by the tail. Once you take Etchu and share a border with Ikko from my experience they WILL attack you, and attack hard. But, you have a secret weapon which is your Monk you can get out lightyears before anybody else. A couple of good rebellions in Kaga or Echizen can give you the breathing space you need to capture Kaga - a magnificent high fertility province with tasty blacksmith! I would consider Kaga as an alternate recruitment center if Uzen is unavailable.
FINANCE
Getting your economy off the ground is very tough as Echigo is not a rich province and the temple you start with doesn't help much. The key is a two pronged approach - firstly you need to secure the Iron trade goods to the North - your trade ships should be pretty safe up here and it will bring in ~1200 per turn with 8 ships there. Secondly you need to keep the number of people you are trading with up so you can make the most of your increased trade income. This is another reason why I didn't go for Uzen, as they make a nice stable trading partner early on.
I'd also strongly recommend getting into Sado as early as possible as it is the only province in the vicinity with a significant tax income. Kozuka is another option, and if your adventures with Takeda and the Southern clans land you this province you can get a very good tax rate out of it by upgrading to a law court. Finally as I mentioned earlier Kaga also offers a significant farming income if you can pry it from the Ikko's cold , dead, hands. Placing Metsuke in each of these three provinces should give you a nice tax base to support your army upkeep, while your trade income is used for further development and recruitment. Try not to spend more than your taxeable income on unit upkeep as all it takes is a wako pirate blockade of your capital and you can slip into bankruptcy which is BAD. Noto Province is also another solid (not exceptional) earner where you can build a market and upgrade the trade port.
AGENTS
A well executed agent strategy is absolutely key on Legendary difficulty as you can't afford to be walking armies off into the fog of war as there is no reload button if they get ambushed! As a general thing I will try and prioritise the following:
Ninja - at least 1 per active army stack. Early on that means just a single ninja and I would actually recommend placing your first sake den in Etchu (as it is a rubbish province and will need the happiness boost too). I'd aslo rank this first agent up in assassination to deal with any Ikko monks who wander into your provinces and for bumping off army generals. While incredibly useful you probably won't have the cash to sabotage armies or buildings early on.
Metsuke - one for each of your key income provinces (Sado/Kaga/Kozuka) really you should be building markets which means you should be building these guys. You won't have the cash to be bribing playing Uesugi so don't worry about that.
Monks - while not overtly that useful they can save you a huge amount of wasted upkeep on garrisoning freshly captured provinces. There is also nothing wrong with demoralising the enemy and if you are playing with the Ikko Ikki DLC at least 1-2 of these guys will be mandatory to keep the Ikko religion spread under control and for sparking the odd rebellion. Given that you will need a temple in every city that plans to produce warrior monks there is no reason not to have a couple of these guys floating around.
RECRUITMENT & ARMY STRATEGY
Firstly - write off getting warrior monks into your army for any intial expansion. They take too much research time and are too expensive (the one exception bieng the free one you receive from research). Instead spam Ashigaru like they are going out of business, plenty of Yari but also some bows for both skirmishign and castle defense. I also added in a few units of Yari Samurai here and there, as the building is a prerequisite for Naginata warrior monks anyhow. Naginata Samurai would be nice, but I personally could never find 2000 koku spare to upgrade my Yari Dojo until well into the game. A great feature of Uesugi is that Kenshin seems to pick up +morale attributes like crazy, he'll also get a helluva lot of battles under his belt - I got him up to 4 stars before I had my 6th province. An army of mostly rank 3-4 Yari Ashigaru, +3 morale, and stand & fight is more than capable of dealing with Samurai stacks in a pitched battle if employed correctly.
I would strongly recommend upgrading the castle in Echigo and using this as a recruitment center (capital gets +1 slot). I would then go for either Uzen or Kaga as your primary recruitment center for melee troops. But early game you are going to be stuck with unupgraded, unexerienced Ashigaru so keeping your commanders alive and getting some command stars is crucial. Also look for chokepoints on the map and construct Castles there - North Shinano is a great example, an upgraded castle with a lot fo bow ashigaru can break stacks coming from the South/West. Likeise Kaga in the West is another great chokepoint. Expanding South into the plains is tough, and not to be taken lightly.
Once you have got the cashflow to incorporate warrior monks into your stacks you should be laughing.
Regarding navies - I tend to ignore them early on playing Legendary as the AI just spams ships like nothing on earth. Build a fleet if you feel your trade nodes are under threat but make sure you aren't spending more on upkeep than you are earning from the node.
REASEARCH
I went straight for the Monastary tech which gave me the free Warrior Monk - that Warrior Monk unit has won at least two battles with it's devastating warcry ability. An amazing force multiplier and you need those techs anyway. The early Bushido techs are nice - but you won't have the cash available to be building or fielding Naginata Samurai so I would prioritise the free Warrior Monk. When picking up the Bushido arts I'd go straight for Way of Earth for the extra amunition (for seige defence) and unit resupply. From there I'd head straight down the Spear tree (or possibly bow if going for lots of bow monks) while filling out some economic techs as needed. Don't forget to establish your supply of Cotton (only one source) for the Yari Master Dojo.
