Green mages

I think Nino is the best infantry green mage currently but she's limited to being a player phase nuke. The others are more versatile but less effective. Another of Nino's big advantages over the others is availability - she is much easier to merge. Some of the others - like Julia - will beat Nino in a duel but Nino is more effective aganist the roster in general.

Spring Camilla and Cecilia are lackluster on their own but can be monstrous with their respective movement type buffs.

Julia and Sonya tend to be better enemy phase units (better at tanking), I'd say Julia is about a 9/10 and if give Sonya a 10/10 for her higher speed. Also both are Reinhardt counter, which if really important.
Nino is a player phase nuke, who can sometimes survive a hit from Hector with fury and +speed -hp with a hp seal, I'd give her 10/10.
Summer Elise is kinda like Delthea in the sense that both have high attack, low hp, the same speed stat (I think), but Elise has around 25 resistance I think, so she won't tank fast mages as effectively as Sonya or Julia. She still can be be a good green mage though. If give her a 8/10.
As for the best IVs,
Nino: +speed -hp (with an HP seal)
Julia: +attack/speed -resistance/defense
Sonya: +speed/attack - defense
Elise: +speed/attack -defense
As for the best green mage, I'd say Nino for offense, and Julia or Sonya for tanking

IMO Nino is the best Player Phase/Attack green mage and Julia is the best option for a defensive mage. Julia w/ Green Tomebreaker is a nightmare to bait out without losing a unit since she ORKOs every green and blue mage and can survive combat with many reds. She also neutralizes Fae (not that you'll run into many), who otherwise can tank and bait out about every green and blue mage. Nino needs player control in order to take advantage of buffing/maneuvering skills/dancing.

Sonya is probably about as good as Julia, but the Fae matchup is why I think Julia is a bit better.

Julia is the best standalone unit. You can run her on any team composition and generally not have to worry about any blue unit and most of the green cast.

If you are willing to build your team to support her, Nino is arguably better; but you cannot just stick her in any random comp and let her go. It really comes down to your other units and your play style.

I tend to favor Julia because so many arena defense teams run Reinhardt, Olwen, or Linde. Baiting and wrecking that blue mage on turn 1 almost always leads to a perfect match. Also, if you're going blade tome, why not abuse hone/fortify movement skills in flyer or cavalry emblem?

Arena Offense:
Nino > Elise > Sonya > Julia

Arena Defense:
Julia > Nino > Elise > Sonya

Nino is by far the best GB+ infantry mage (almost strictly better than Elise), which makes her the best offense choice because blades are the best thing you can do on offense. Julia wins on defense because her magic tankiness coupled with a strong tome that doesn't require buffs, on top of a sky high atk stat make her the best on defense.