The protagonist is female. After her parents died in a car crash, leaving no will, her relatives try to take the fortune left. After going for a hike, she returns home and finds she can teleport between Earth and another world. Due to the monsters that she encounters there, she seeks out gun training with an American mercenary group (Black Hawks or Black something) to kill any monsters that may threaten her. When the army of a different kingdom with monsters and dragons threatens to destroy the kingdom she lives in, she goes and hires the mercenary group to save the kingdom.
You might be looking for Saving 80,000 Gold in an Another World for Retirement.
An 18-year-old girl who lost her family in an accident, Yamano Mitsuha falls off a cliff one day and transferred to a different world with a civilization level of medieval Europe. Mitsuha who discovered it was possible to go and return to Earth after a deadly fight with wolves decided to live in both worlds. 「For the sake of security in old age, I will aim for 80,000 gold coins!」 I will try not to let strange things circulate and distort the progress of the world, but I won’t hold back for the sake of my easy life and safety! While carrying three handguns along with words and deeds that appear decent, in her head, Yamano Mitsuha is a sly girl. Making an effort to make money even with a small body that looks like a child to foreigners! Oh, my secrets are too dangerous, you said? It’s fine, it’s fine! I’ll transfer away when push comes to shove!
The protagonist is a female. Parents died in an accident and her uncle tried to steal the inheritance. She falls off a cliff and teleports into another world. She gets weapons training from some US military group, not sure about the name. The later parts about the kingdom and mercenaries I'm not sure about.