Off the top of my head, there's probably a lack of usable runways, so likely flying some sort of Vertical Take-off & Landing or Short Take-off & Landing. Perhaps some new generation of Harrier JumpJets...

But with the alien invasion angle, 80's, and anime - perhaps some sort of transforming aircraft based partially on alien tech like they had in the anime Robotech / Macross? It's a plane, it's a half-plane with legs, it's a 50' tall mecha with a gun. 

Watch out for tanks.

Just a thought.