It's not necessary to max out all your characters' stats if you're playing on Normal/Casual (not even on Hard, really). Most of the characters fit well with their assigned class roles, but second seals just give you added options. For example, you might want an extra myrmidon rather than a thief, or something like that.
However, not all the characters are cut out for the other classes available to them, so I'd check the Fire Emblem wiki (http://fireemblem.wikia.com/wiki/List_of_characters_in_Fire_Emblem:_Awakening) if you're interested in straying from a character's usual promotion path.
Personally, I never used second seals except for Panne and maybe one other character. Most classes have their uses, and I never felt the need to double down on second seals except to bring a promoted level 20 character back down to 1 (they keep their stats, but you can continue to level them that way.)
Basically, I leveled my characters to level 20, promoted them, leveled them back up to 20, and used a second seal on them to "re-promote" them back into their class at level one. I'm not saying that's the "right" way, but that's how I did it, and my characters were more than capable of talking on the final boss. Hope that helps!
Edit: If you do check out the character Wiki, be mindful of spoilers. Skip the "profile" sections. The "overall" and "re-classing" sections have the spoiler-free information you're looking for.