On the battlefield.
Okay, so first off I completely fail at this strategy type stuff, and while what I'm about to say is probably entirely pointless––and even possibly a complete waste of time––I do it just because I like doing it (which probably explains why I have 800+ hours played on this game). Basically it starts with Cordelia in her base class as a Pegasus Knight with the plan of keeping her as a Falcon Knight once I have all the skills I need/want from her other reclass options, with the option to change the skills around as I see fit.
"I am yours to mold as you see fit."
Because of her low level when she first joins your army it is best to grind out some experience against some Risen to get her a up few levels. Once she reaches level 20 I like to promote her to Dark Flier first in order to get the Galeforce skill as soon as possible as it allows her a second turn if she kills an enemy, resulting in faster experience gains and less bad guys trying to kill you––plus it's a super skill to pass down to her kids (even if they can technically get the skill themselves, but this saves them from having to get it later). After I have that I like to grab Sol, from the Hero class, and Lifetaker, from the Dark Knight class, both of which are awesome healing skills which make Cordelia that much harder to take down. Other good skills to have include Bowbreaker, from the Bow Knight class, to help against bows and Armsthrift, from the Mercenary class, so her weapons last longer.
Despite Cordelia's slow magic growth, Vengeance and Tomebreaker, from the Sorcerer class, can also be useful to grab––the latter more so as to better protect her against wind magic––so it would be a good idea to put her in this class to grab them. If her magic seems too low and she can't deal much damage, using Spirit Dust to up her magic or using Arms Scrolls to up her weapon skills would help fix that. Supposedly Slowburn, from the Dark Knight class, is a good skill to get as well, but personally I never really cared that much for it to actually use it. Regardless, you'll get it anyway if you choose to go for the Lifetaker skill so the option to use it is always open if you find yourself needing it (which I never do because by this point the baddies can never hit me and I'm double hitting them).
So obviously that is a lot of skills I listed just now, and because you are only allowed five skills at any given time that means you won't be able to use some skills. As such it can be tricky to decide which ones you'd want to use. For me personally I like to go with Galeforce, Sol, Tomebreaker, Bowbreaker, and Lancefaire (from Falcon Knight) to keep her fairly well rounded, both offensively and defensively. What you choose to use, however, is entirely up to you, but this is what I like to go with.
As an added bonus here is a screenshot of Cordelia's stats and skills from one of my playthroughs.