A few suggested roles if people are unsure what kind of character to create. This is by no means an exhaustive checklist where every niche has to be claimed and filled, it's meant more to give people an idea of the kind of roles that might be helpful on a team devoted to countering giant monster attacks.

Military personnel- officers from land, sea, and air branches to coordinate with the locals and work out the best weapons and tactics to bring into play in combat. Keep in mind you'd have to work with what the country under attack has available- not every country can whistle up massive amounts of firepower. Some don't even have military forces.

Emergency management- Someone with experience in efforts like evacuations, putting out fires, treating massive numbers of wounded, digging survivors out of rubble, handling chemical spills, that sort of thing. Maybe they come from a large city's fire department or something like [url=https://en.wikipedia.org/wiki/Technisches_Hilfswerk]Germany's THW[/url]. Same issues as above, so quick thinking and improvisation are key again.

Biologist/ zoologist- Definitely handy if you want to understand these new animals. Analyzing behavior and functions of kaiju, a new science. This is far from a rear-echelon role, expect to get up close and personal with the beasts.

Engineer- The person responsible for building the tools to deal with this new threat. Don't expect to roll out Mazinger Z in a week, though- there's bound to be prototypes, testing, trial-and-error. 

Hopefully that gets some ideas flowing!