Well, for the male Avatar...
Name: Most likely my username, or my real name.
Best Stat: Skill, Speed, Luck, or Magic, depends on what his worst stat will be.
Worst Stat: Defense/Strength if Skill is Best Stat. HP/Defense if Speed or Luck is Best Stat. Luck, Defense or Resistance if Magic is Best Stat.
Class: Warrior, Berserker, Dragonmaster, Sage, Sorcerer, Battle Monk, or Demon Fighter. He will also reclass to get a variety of skills.
Weapon Focus: On Axes and Magic (specifically Thunder and/or Dark Magic).
Skills: Weapon Saver and Limit Breaker. The other skills will depend on the situation, though he will likely have a combination of Luna, Crimson Curse, Vengeance, Wrath, Quick Slash, Counter, Magnificent Flame, Life Absorb, Tome Expert, Axe Expert, or All Stats +2.
Lover: Lissie, Miriel, Sariya, Anna, Serge, Tiki, Noire, or...
For the female Avatar...
Name: Depends.
Best Stat: Luck, Speed, or Magic, depending on what her worst stat will be.
Worst Stat: HP/Defense if Speed or Luck is Best Stat. Luck, Defense, or Resistance if Magic is Best Stat.
Class: Grandmaster, Hero, Dragonmaster, Sage, Sorcerer, Dark Knight, Battle Cleric, or Valkyrie. She will also reclass to get a variety of skills.
Weapon Focus: On Swords, Axes, and Magic (specifically Thunder and/or Dark Magic).
Skills: Weapon Saver, Limit Breaker, and Lightning Speed. The other skills will depend on the situation, though she will likely have a combination of Luna, Crimson Curse, Vengeance, Magnificent Flame, Life Absorb, Sword Expert, Tome Expert, All Stats +2, or running a Cry/support set.
Lover: Chrom, Henry, Basilio, Brady, Jerome, Loran, or...
I hope I manage to completely fill up the support library in this game eventually. it's pretty huge...