I plan to have my characters be on one of their base class's promotion with a few exceptions, such as my Avatar being a Sorcerer (I defined his asset and flaw as Mag and Str, respectively, so I basically traded swords with dark magic).
So far, I have two characters at max stats: Owain (Swordmaster) and Ricken (Dark Knight).
Donnel (Bow Knight), Chrom (Great Lord), Lucina (Great Lord), Sully (Paladin), Sumia (Dark Flier) and Henry (Sorcerer) are pretty close to max stats. They all have one or two stats 1-5 points away from the limit, something that can be fixed with stat boosting items I have been obtaining through Risen challenges and Anna's shop.
I went through reclassing to reach such high stats. Owain has Donnel as his father and I reclassed him to Villager to learn Aptitude, then reclassed to Mercenary and learn Armsthrift (Luck*2% chance of not counting a weapon use). As a Lv 9 Swordmaster, he hit max stats with 51 Luck. The result? Weapons have infinite uses and he's an authentic killing machine. His inventory consists of Levin Sword, Brave Sword, Balmunk (the Spd+5 bonus may be enough to double certain foes) and Amatsu (for ranged physical attacks).
His skillset is Astra, Vantage, Swordfaire, Armsthrift and Patience (I might replace this one with Sol, but having extra hit and dodge rate when under attack isn't bad at all).
I had Chrom, Sumia and Ricken reclass to Great Knight so they could have the Luna skill. Sully and Lucina have Astra and Vantage due to being previously classed as Myrmidons.
I actually plan on doing this to all my units, so it's going to be a long time until that is done. Completionists will really spend a long time on this game. If you want to unlock all support conversations, you need to do a lot of playthroughs, considering the amount of possible marriages.
(Didn't expect to write such a long post.
I really like the reclassing system of this game as the possibilities for unit customization are almost endless.)