I'm not of Scandinavian descent, but I live in Norway and speak Norwegian, and both languages are very similar (knowing one, you can understand and kind of imitate the other). Knowing a couple of other languages that I can use as reference (German, Russian, Arabic, and most importantly Norwegian), I can tell you that picking up on a bit of Swedish won't be hard. The Scandinavian languages are very close to English, with Danish perhaps being the exception based on its very odd pronunciation.

Some pointers: Even though Swedish has simple grammar, I think you should focus on the pronunciation, as its eccentricity can be a bit of a challenge to master. Also note that if Swedish urban slang and/or rural dialects are as bad as in Norway, you could be having a hard time understanding anything.
More so with Swedish than a lot of other languages, I think your choice of means for theoretical learning is less important than actually having a Swede to communicate with, especially verbally.