Key Provinces on the Campaign Map

[Poulp']

As Oda, holding the bridge in Suruga province is critical once realm divide hits; it directly protects 4-5 cities while I concentrate my northern defenses in South Shinano (the stone makes it easy to upgrade the castle). As I expand West, upgrading the castle in Omi is important too; the shogun's army never siege the town, but losing Omi is losing my main crossroads and the fastest way to switch armies between the Sea of Japan and the Pacific Ocean.
North Shinano is a crossroad too, but not as important as Omi; you can lose the province and as long as the bottleneck in South Shinano holds, your heartland is safe. I never saw an army bypass the castle, they sometimes raided the farms, but they always turned back to siege it.
Finally, Settsu province is important if you want to further strengthen your hold on trade nodes; though it's not critical, it makes the sending/repairing of fleets 3 turns faster.

As Date, I make the conquest of Fukushima my top priority; if someone wants to go further North, they must pass through these lands. Then I'm sure I can clean the North from Mogami influence with no outside interference.

As Shimazu, I hold the landbridge in Buzen while a fleet-in-being is anchored in Bungo. Obviously, the whole of Kyushu was already in green.

With any clan, holding on Mimasaka and building a whole militaro-industrial complex prior to realm divide makes everything easier. In two moves, you can cut the whole peninsula and still spam units like Ford would produce Ford-Ts.

Edit
I (roughly) traced the roads, but screengrabbed the map from here http://shogun.bitcrumbs.com/, credits to the author(s)