Yay, a language post!
The vos tense and shh (or zh like zsa zsa gabor from the older generations, listen for the difference) sound for ll/y are the differences foreigners notice first. But they are far from the only differences. How often do you ever hear the present perfect spoken? (Yo he ido, yo he probado, etc.) Almost never. Or this particular future tense in everyday speech: Iré, saldremos, etc. No, usually you will hear voy a ir or vamos a salir. And let's say you want a side salad instead of papas fritas with your meal, because you're a cheto bastard from Palermo Island and sometimes you can pull that shit there. You would say, perhaps: Con ensalada en vez de papas fritas, ¿puede ser? Even that "puede ser" is re argentino. In many (most?) other countries they would just say "por favor." Also, try going to Colombia or Spain and saying papas fritas. Nope. Try papas francesas and patatas fritas. Spend enough time in BA and you will pick up expressions and grammar that you may not even realize are specific to the region. I could go on, as I'm sure anyone who has spent any significant amount of time here could.
So the OP could learn nothing but Argentine Spanish and lunfardo, and yeah, people in other countries would understand for the most part.* But would he understand them? I took a FANTASTIC class through Expanish at UBE in 2008 with a great porteña teacher named Melania. It was an intensive grammar course in which we reviewed every single grammar tense and a bunch of neutral Spanish**, and then went over how people speak in Buenos Aires. So we learned neutral Spanish grammar, but also had several classes over the local dialect. Five hours a day, five days a week for a month. The OP could certainly specify what kind of class he/she wants.
*Not always. I met several Argentines when I was traveling the Colombian coast who could barely understand or be understood themselves when talking to the locals. I have never heard faster Spanish than in Cartagena, and oh my God, the slang. Made even porteños sound slow after, which is nuts.
**It does exist, at least in the fictional realm (and see what syngirl wrote above). Watch Los Simpsons. Although they do give that bee guy a Mexican accent.