Avatar: The Avatar can give Owain some good stats but the asset and flaw chosen can affect Owain in many different ways, although the flaw shouldn't affect him surprisingly as much as it would other children. His magical abilities with a good magic growth as well as passing down Ignis can make Owain an interesting unit, even in his Myrmidon base. He will also give him an incredible class pool that makes him a second Morgan.
Frederick: Frederick passes down very balanced growths supporting his defense although he'll hurt his magic and luck rating. He can pass down Luna, allowing Owain to deal some much needed extra damage. Owain can also inherit Dual Guard+ and Dual Support+ and make him a strong support unit. Owain can also obtain a weapon breaking skill from Frederick's Wyvern Rider class set against either swords or Lances. Stahl can offer the same cavalier related abilities and perhaps give Owain better starting stats since Frederick's stats wind up rather low when compared to other mounted units.
Virion: Virion will offer a high starting skill for Owain and nurture his high magic and resistance. From Virion's Archer class, he gives Owain access to Hit Rate +20, which is a very useful ability for any character, and Bowbreaker to avoid being picked on by archers. The Mage class can be useful for Owain's repertoire given that he gains the Dark Knight promotion which has Lifetaker for a stronger life regen as long as he kills units. The other class Owain gains is the Wyvern Rider which becomes the Wyvern Lord and Griffon Rider, both of which give him more utility skills like Swordbreaker and Lancebreaker to be a unit killing specialist.
Donnel: Donnel gives Owain a boost to his luck allowing him to hold an impressive 51 cap in luck and is the only way to achieve this without having a Luck asset Avatar marry Lissa. Donnel will pass down the ability to have Villager as well as Mercenary and Fighter, the last two of which are great physical classes for him to exploit. Because of his 51 cap, Armsthrift will ensure that his weapons will never break once his luck reaches 50. This serves well to preserve Owain's Missiletainn, any regalia weapon, or forged weapons. Owain gains only two new promotions as a result of Donnel's class inheritance, being the Bow Knight and Hero classes. Hero gives Sol for more regen options and Axebreaker give more bonuses when attacking axe users. Bow Knight gives Bowbreaker to dodge archers if Owain is a sword wielding class. Villager is not necessary to reclass into given the low stats of the class. Aptitude is a good skill for Donnel to pass down, but if Donnel and Lissa have been well trained before recruiting Owain, then this skill loses usage. Underdog only works when Owain is lower level than his enemies so it is very situational.
Ricken: Ricken is an interesting choice as it passes down classes in which it allows Owain to be both a offensive and supporting threat. Ricken passes down Archer, Mage, and Cavalier. Owain gets a large boost of magic due to the modifiers Ricken passes down, making a Sage with a magic stat of 51. This can be bolstered by Tomefaire and Limit Breaker (if the player has the DLC) essentially giving him a magic stat cap of 66. It can become even more threatening as Owain can receive Luna, which can make him very dangerous if his magic stat is capped out and fighting against an enemy with high resistance. Owain can also play the supportive role with Ricken as his father. He receives Dual Guard+ from the Great Knight class as well as Defender from the Paladin class. In addition, he can also gain Aegis from the Paladin class, reducing damage from bows, dragonstones and tomes by half, and due to his good skill stat he should activate this skill quite frequently in battle. Combined with Counter, it can be very helpful in intimating other players as they will either risk dealing reduced damage or use physical-orientated weapons to bypass Aegis and risk being hit with Counter. However, as a result of Ricken's modifiers, Owain's strength and defense caps will go down a bit, making mixed classes like the Dark Knight less useful. Despite this, the remaining stat modifiers Ricken gives to Owain makes him very powerful and gets rid of most enemies with little effort.
Libra: Like Henry, Libra passes down Dark Mage, but the only other class he passes down is the Mage class. Should Libra still be a War Monk by the time Owain is recruited, Owain will inherit a slightly increased magic growth, which is already high thanks to Lissa, as well as a bumped Strength growth, too. Libra also offers a high resistance modifier for Owain, and with Owain as a Sorcerer, makes him hard to take down with magic. Vengeance, Vantage and Wrath all activate for Owain at half HP, making him even harder to kill as Vantage will allow him to move first, almost certainly killing what attacks him, and should Owain be placed in a critical condition, both parents can possibly pass down Renewal, giving him even more buffing.
Henry: Henry is very similar to Libra especially in terms of skills. His mods tend to be more balanced than Libra, having a good stat distribution and no negative modifiers. He passes down Thief, and, most importantly, Dark Mage. As a Sorcerer, Owain can tank using Nosferatu or Aversa's Night tomes and Vantage, making him very hard to kill. Owain can inherit Lifetaker from Henry for longevity, Lucky Seven to bolster his Hit/Avoid for the first seven turns, or Tomebreaker to be a good tome-using killer.