You can marry any character in the game as long as they are the opposite sex. Other characters have specific people that they can marry and I don't really feel like listing all of them for every character, but the general rule is that if they can marry someone other than you, then they can marry anyone in their age group.
Marrying isn't that hard at all, just pair the 2 people you want to marry and after a few stages, they'll marry. I will note that if you don't marry Chrom (the other main character) by Chapter 11, he will marry someone automatically for story reasons. But you can take however long you want with everyone else.
You can go for optimized children, but it doesn't matter that much in the first play through so just go pair whoever you want. (And the children are all beasts no matter their parent so it doesn't matter that much. Besides if the 2 parents go well together, the child's hair color is dependent on the father so a lot of people go for whatever hair looks the nicest on the child
)