If Desplat returns to do the sequel, you'll likely hear variations on those same themes.
I like the first track well enough, even if it really isn't one of the stronger themes of the series. It's still the theme you look forward to hearing the most in the movie.
You hear variations of the "Godzilla!" theme in the last 35 seconds of "Two Against One," a stronger version of it throughout "Last Shot" and another cool variation of it (that was cut from the movie) in the first 10 seconds of "Godzilla's Victory".
I wish they included the version where the helicopter takes off from the aircraft carrier with Ford in it. It's not much different from "Godzilla!" and "Last Shot" but it irks me when variations, even if very minor, are cut from soundtrack releases.
So with that, I guess my answer is "Godzilla!", "Two Against One", "Last Shot" and "Godzilla's Victory". I also enjoy "Back to the Ocean" a lot. It's a great ending piece in the same vein of Ko Otani's feel good ending tracks. You can also make out the "Godzilla!" theme in that track around the 2:44 to the end of the track.
"'Nostalgic' does not equal 'good,' and 'standards' does not equal 'elitism.'" "Being offended is inevitable. Living offended is your choice."