ZeroZet really nailed your best draws, as well as the key points of leveling. Only things I might add are Remnant Vanquish 3 is inferior to RtR for unit leveling but is better for Prince leveling (to raise max charisma) and doesn't hurt your gold as much.

Once you've snagged Katie and Cloris from those special missions, I'd suggest leveling:

Katie > Claire > Alissa/Iris > Bernice > Mehlis/Elizabeth > Lilia/Kerry > Leanne > Sophie

Reasoning:
Katie: Excellent early blocker, and a UP generator. Unless you pull Zenobia or Jerome, no reason not to get her up.
Claire: Archers are great for early game damage and one of the core classes (along with Healers and tanks)
Alissa/Iris: cheaper vs. stronger, but healers are a must, so get these two up. Camilla is great if you manage to pull her.
Bernice: The last of the 3 core roles, Bernice is one of the best tanks in the game (and the most durable gold in the game against physical damage), get some levels on her and she will serve you well
Mehlis/Elizabeth: Liz is insane against lightly armored units and moderately low UP cost, Mehlis is the best gold mage and in the absence of plat+ mages will be your go-to source of late game magic damage
Lilia/Kerry: You'll need duelists down the road. Kerry is cheaper and can be a UP ramp (each killing blow gives 1 UP and she gives more UP back upon withdrawal than normal), Lilia is extremely tough (she's the defensive plat princess, while Sherry is the offensive one) and slices up armored enemies like butter since her attacks are magical; one downside is Princesses are fairly expensive deploys
Leanne: Secondary tank is good to have, and in the absence of samurai, dark knights or advance guards, Leanne fills the role well enough
Sophie: 3 reasons she's so low on the priority: blacks are expensive to raise down the road, and she doesn't need very many levels to be a wrecking ball and super lightning rod. 3rd reason is it's cheaper to feed rainbows to lower levels and she's a prime target for your rainbows since her skill level determines how much blocking she'll do.

Others, feel free to offer your own counter-arguments for this leveling priority list.

Oh and I assume you know not to use silvers for CR/SU since you'll need them for CC and AW