Though eventually I plan to learn at least some of all three, and I am currently working on both Nihongo and Hangul, I am not sure learning them simultaneously is always a good idea.
Yes, there are similarities, but I find when I start to speak (as opposed to reading aloud) I am prone to use words from both languages in the same conversation. That's ok if the other person speaks both, but its a problem otherwise. Sumimasen and jeonmanhaeyo do not belong in the same sentence.
But that may just be my own quirk. I had the same problem when I began studying German while writing a thesis in French. My professor was very amused by my sentence construction of either German nouns with French verbs or French nouns with German verbs. But I had a hard time stopping it till I gave up on the German.