My first game was Shimazu too. By the time I reached Shinano, I already outumbered the Hojo. The Hojo was reluctant to attack me after I enflicted heavy losses on them in one battle.
I find Shinano easy to defend. You don't even have to deploy at the way back of the map. You could just make an ambush from the mountains at the left and right at the beginning of the battle. Since the cliffs on both mountains prevent any movement there, you would have to attack parallel to the cliffs. Once your down the mountain, you'd be attacking the enemy on both sides because the AI always starts at the center back. The map is a good place for a defender to rush in.
In my early stages of the campaign, I usually defended my provinces with few armies in order to attack enemy provinces with more armies. My basic defending army was 2 units of archers, 1 ashigaru unit, and 1 cavalry unit. I used the cavalry to flank and then chase the fleeing enemy. Since I was outnumbered by at least 2 to 1 (and this wasn't multi), I camped on a steep slope. It's highly effective when you could kill many with few of your men.