Hi Namu
I would personally recommend that you start with Japanese for the following reasons:
1. As you yourself pointed out, with your Korean background and similarity in grammatical structures, you will find at least spoken Japanese much easier to pick up.
2. If you are going deeper and delving into the written form, this could open up the possibility of paving the foundation for a 4th language.
Japanese written form is divided into 3 main groups* : Hiragana,Katakana & Kanji. Kanji uses chinese characters that more often than not have similar meanings to their chinese roots, which could open up the possibility of learning Chinese at a later date.
As for intonation and accents, you can always watch Japanese Anime with English subtitles for practice.
*There is also Romanji, which many find easier to pick up, but if you are going for a deeper understanding of the language, I would recommend that you at least learn Hiargana, Katakana and a decent amount of Kanji (say, 200 to 500 words?)
All the best in whatever language you finally choose.