I tend to make marriages that will strengthen my descendent's Martial skills, SD. It is not uncommon in the mid- and late-game to have a series of heirs that are 15+ Diplomacy and 0 Martial. Any trait that can be inherited to promote Martial skill (e.g., Misguided Warrior; Busho) is to be sought, as this frequently is the only Martial ranking one's heirs will have.
For female descendents, I look for politically opportune marriages. From time to time clans will lose all male sons and vassals in combat; sometimes you can marry into these before the last male dies and inherit a kuni or two. Also, marriages give a positive increase to the opinion of the other clan to yours, making it safer to avoid or postpone going to war with them.
Lastly, there are a few clans (like the Tozawa & Honma) which lack vassals and are few in mumber. Marriages can strengthen them as an ally, and potentially lead to your gaining their kuni if their lineage dies out.