Chinese vs Korean
Learn Chinese and Korean at the same time
Chinese and Korean are unrelated, but Korean absorbed a large Sino-Korean vocabulary that once was written in Chinese characters (Hanja). Grammar and sound systems differ sharply: Chinese is tonal and analytic, Korean is non-tonal and agglutinative.
The short answer
Possible, and the Sino-Korean overlap rewards it: Chinese roots help you guess Korean vocabulary. Grammar and pronunciation share little, so interference is low but so is transfer. Build one to a stable intermediate level first, then add the other.
The verdict
Workable: Chinese first makes Sino-Korean vocabulary click. Korean first gives little help with characters.
Closeness score
6 / 30
Mutually intelligible?
no
Shared vocabulary
Roughly 60% of Korean dictionary vocabulary is Sino-Korean, though less in everyday speech
Which first?
Chinese first unlocks Sino-Korean vocabulary.
Kungfucius says: Korean borrowed the vocabulary and returned the characters.
Side by side
diànhuà전화 (電話)
jeonhwaSino-Korean reading of the same compound.
xuésheng학생 (學生)
haksaengKorean keeps the final -k that Mandarin lost (學 hak vs xué).