Well, if you just want to grind your characters up for levels then the following DLC are the best:
Lost Bloodlines 2: for the Dread Fighter class (you'll have to do the map multiple times for multiple of the class item)
Lost Bloodlines 3: for the Paragon ability scroll (you'll also have to do it multiple times)
Smash Brethern 2: for the Bride class (same as above)
Smash Brethern 3: for Iote's Shield (same as above and only really useful for any flying units)
Rouge and Redeemers 3: for the Limit Breaker ability (same as above but is useful for all units you plan on using)
The Golden Gaffe: for gold
EXPonential Growth: for very quick leveling
Now, if you want to enjoy just conversations and interactions between the Awakening crew, you should get:
The Scramble Pack
Future Past Pack
As for the best combination of parents and classes, that really depends on your preferences but some characters are better in certain classes like. I'll list what I used during my playthrough and you can use it as a guide or base or whatever:
Chrom (Great Lord) x FeMC (Grandmaster) = Lucina (Great Lord), Morgan (Grandmaster)
Frederick (Great Knight) x Sumia (Dark Flier) = Cynthia (Falcon Knight)
Stahl (Great Knight) x Cordelia (Falcon Knight) = Severa (Hero)
Vaike (Warrior) x Sully (Paladin) = Kjelle (General)
Gregor (Hero) x Cherche (Wyvern Lord) = Gerome (Wyvern Lord)
Lon'qu (Assassin) x Panne (Taguel) = Yarne (Taguel)
Gaius (Assassin) x Nowi (Manakete) = Nah (Manakete)
Libra (War Cleric) x Tharja (Sorcerer) = Noire (Bride)
Ricken (Sage) x Maribelle (Valkyrie) = Brady (Sage)
Henry (Sorceror) x Miriel (Sorceror) = Laurent (Sorceror)
Virion (Bow Knight) x Olivia (Dancer) = Inigo (Hero)
Donnel (Hero) x Lissa (Sage) = Owain (Dread Fighter)
I wouldn't say these are the best classes but they work pretty well when I play but like I said it's all up to you. I hope this helped you
What other dlcs should I get?, pls help 