梅雨 (Rainy Season) Preparation Tips

Hello everyone! I really don't post on Reddit basically at all, but I figured this may help me before I do something massively wrong.
For starters, I have been in Japan many times for extended periods as my Grandfather was Japanese. But now, I moved here myself a Month ago.
I might not be super rich, but I'm not super broke either. I can afford what is neccessary for preventing Mold/Bugs and more.

So I'm renting a House in Kure, Hiroshima Prefecture. It was not quite an Akiya, but it is in an older district. The House is old, has two Tatami rooms, is extremely open (barely any doors inside, this is important). The Bathroom has no 24 hour fan, there is no Air Conditioning. It is a pure, shitty, wooden house. (Guess why I barely pay rent lol).
I was ready for everything that comes, since my Grandfather had a similar house. But now, I have to take care of it all on my own.

With all of that above considered, what do you think I should be getting or doing to prepare for Tsuyu? To keep as many big bugs (Mukade, Spiders) out as possible while also preventing Mold growth in a House that barely has any doors.

Should I get a dehumidifier? If so, for how many Tatami mats size? Or is an Aircon better? Both would surely work, but I want to save a bit of money.
Do i open windows on Dry days only or on wet days too? Do my old Amido (bug nets) actually keep bugs out when I open the Windows? Should I leave my bathroom door open or closed?
So many questions.

Shoot all your tips and answers!

by EvelineAkagi