Personally, I make every character go through all of their base- and promoted classes, so that they have maximum utilisation.
First generation classes.
Chrom: Great Lord (Or Bow Knight due to Bowfaire);
Lissa: War Cleric (She can use a Bolt Axe and she needs the extra Defense);
Frederick: General (Or Great Knight, because he's dang awesome as one!);
Sully: Swordmaster (She's better off as one);
Virion: Sniper (Or Sage, due to his Mage lineage);
Stahl: Bow Knight (Swordfaire and Bowfaire make this a very solid choice);
Vaike: Berserker (Let that Axefaired forged axe of Hector smash those skulls);
Miriel: Sage (She really rocks those tomes);
Sumia: Dark Flier (Solid reclassings for a solid set-up);
Kellam: Great Knight (Or General, Because invisible wall!);
Donnel: Warrior (He's most balanced like this and a freight train to boot!);
Lon'qu: Swordmaster (Creates total awesome with Sully when they double Astra VS a General);
Ricken: Dark Knight (Or Sage. Looks cute and is deadly, like Miriel);
Maribelle: Valkyrie (Amazing support unit);
Panne: Taguel (Just keep her pure to her roots, she'll do just fine);
Gaius: Swordmaster (or Assassin, I'm usually looking at the Faire-skills here);
Cordelia: Falcon Knight (There's so much win in her build, I don't even know where to begin!);
Gregor: Hero (Axe- and Swordfaire, Armsthrift and Astra...damn dude!);
Nowi: Manakete (Don't fix the broken...just...don't);
Libra: Sorcerer (Or Sage. He manages quite well in both);
Tharja: Sorcerer (Most certainly yes!);
Anna: Sniper (Or Sage. She just doesn't do well as a Trickster);
Olivia: Falcon Knight (Or Dancer. If you don't want to lose Dance, pick the latter.);
Cherche: Wyvern Lord (Because we don't wanna lose Minervykins);
Henry: Sorcerer (Henry is an utter beastly Crit-Hitting man!);
Say'ri: Swordmaster (Or Assassin, they're both good);
Tiki: Manakete (See Nowi);
Basilio: Berserker (Muscle! Strength! Hit like a truck!);
Flavia: Hero (Not broken, don't fix);
Gangrel: Sorcerer (He just doesn't manage a Trickster, Just like Anna);
Walhart: Conqueror (This beast needs no change, he needs to keep on beasting!);
Emmeryn: Sage (Best Sage around, no need for changes);
Yen'fay: Bow Knight (Pick up Bowfaire along the way and you've got a solid unit);
Aversa: Dark Flier (Or Sorcerer, both work and Sorcerer has an extra slot to work with);
Priam: Hero (Or Warrior. Whatever suits your taste.);
The pair-ups I've had for the children characters were (in Lunatic+)
Chrom + Sumia = Lucina and Cynthia.
Virion + Lissa = Owain.
Frederick + Olivia = Owain.
Henry + Maribelle = Brady.
Gaius + Sully = Kjelle.
Stahl + Cordelia = Severa.
Gregor + Cherche = Gerome.
Lon'qu + Panne = Yarne.
Kellam + Miriel = Laurent.
Ricken + Tharja = Noire.
Donnel + Nowi = Nah.
My own Avatar wasn't married. If I had to, I'd go for Tiki (Asset Defense, Flaw Luck)
Final Classes for Children Units.
Lucina: Great Lord (Or Paladin. Lancefaire brings her to a better place rather than just Bowfaire.);
Cynthia: Dark Flier (Or Bride if you have the DLC. Her balanced stats and 3 Faire abilities make her a very potent Bride);
Owain: Any Magical Class (Or Dread Fighter if you have the DLC. He's a top-notch Galeforce Dread Fighter!);
Inigo: Hero (His Faire skills and his big diversity of abilities and Galeforce make for a fantastic unit);
Brady: War Monk (Axefaire, Healtouch and a huge amount of abilities + Galeforce.);
Kjelle: Paladin (Thanks to Gaius's classes, she can finally fully optimise her Mother's dream with Lancefaire!);
Severa: Paladin (Or Bow Knight, she'll wipe the floor all across the battlefield);
Gerome: Hero (Or Wyvern Lord, Because Minerva is not to be lost forever and their Dual Support+);
Yarne: Taguel (Very quick, Astra, Wrath and Deliverer. Seems like succes!);
Laurent: Sage (With access to Healtouch, Pavise and Dual Support+ and Tomefaire make for a very potent Sage);
Noire: Sorcerer (Both She and Laurent have a base 50 Magic, Luna and Tomefaire, Did someone say Valflame?);
Nah: Manakete (With a base 50 Luck, her Dragonstone will never die out!).
Morgan: Manakete (enormous diversity like her/his Father/Mother, Counter or Axefaire for Female Morgan, Galeforce or Dual Support+ for Male).
And there you have my opinion ^_^ Hope this helps ^_^
