Great thread, some really interesting ideas on here. I found shimazu easy early on because of the natural defensive qualities of kyushu. With Mori I always tried to push up to Nagato then take the small Island as long as the rebels aren't too strong.
Biggest problem I found was that the computer was much quicker at forming alliances. I'd find everyone allied against me before my emissaries had even found a daimyo to ask :)

I always tried to take shinano as the drain on enemy troops was massive considering wha it took me to reinforce it. Generally two or three YS plus 3-4 SA to start off with. Add naginata as soon as you can and maybe stash a warrior monk or no dachi unit for fun. line up the archers along the top of the right hand cliff face. Use YS (and naginata) to hold off direct attacks while the archers do their business. If you have a daimyo then putting him in the valley draws the enemy troops in and your archers will cut them to pieces. Even if they do suvive and try to chase him up the hill you'll have had loads of time to move in some troops to attack them and the height bonus added to their exhaustion makes light work of them.

It is easier to just take Mutsu, dewa and echigo, then take Hitachi for a troop production facility and finlally take musashi to have 5k coming in a year before expenses.