From your pics, I think we have a similar hair texture. I got a magic perm one summer a few years ago and it actually worked pretty well, but it was way more expensive than I was expecting so I don’t think I’ll do it again.
Before I had it done, I was told that it would be around 150,000 won. However, my hair is different than normal Korean hair so I ended up having to use more products and it took extra time. They also didn’t include the after-treatment that’s needed in my quote. It ended up being 300,000 won in the end ㅜㅜ
Instead, what I do is regular deep conditioning to keep the frizz down and straighten it out. I know it might sound kind of weird, but covering your hair in mayonnaise once a month actually helps a lot. I wet it first, then cover the hair in mayo, leave it for 20-30 min, and rinse it out. Then, I use a circular brush to blow dry it straight. Normally, it keeps it pretty silky for a few weeks.