Cherche or Gerome for an offensive green flier?

Lucina.

For the tempest? Gerome for sure, since he gives a bigger bonus to score, and Fortress Defense can be swapped out for something more offensively oriented like Death Blow or Attack+.

Outside of that, Cherche's got min-maxing potential, so it might be worth it to wait out for one with better IVs and work on inheriting skills for her in the meantime.

gerome cuz hes the cutest boy and he has a cool mask.

Cherche. You can build her now and merge into a better IV when you get one. Gerome will give you a nice bonus this Tempest Trial, though, and will be useful for Arena Assault with the Poleaxe.

Strictly speaking, Cherche completely outclasses Gerome with accounting for boons/banes due to her higher atk stat and higher merging potential due to being available as both 3* and 4*. I'd say just wait until you pull a +ATK/-RES or -SPD Cherche since she comes up so frequently when you're trying to summon greens.

She is a total beast. Doubles just about everything, even takes out res armor ohko (if shes taken enough damage) and is bulky. Way better than gerome (outside of the current TT).

I'd say Cherche because of merge potential and Gerome is great fodder for his weapon