Should you learn several Arabic dialects or Standard Arabic only?
There are five basic dialects in the Arab countries.
1. The Levantine dialect: It is spoken in Syria, Lebanon, Jordan and Palestine, and it is the most widespread, due to the situation in Syria today. Most of the people you will meet today in the world are Syrians. It is a dialect widely spread in the Arab world also because of television series, and the presence of native speakers in all Arab countries.
2. The Egyptian dialect: It is spoken in Egypt, a dialect that is also widely understood by all Arabs, because of the Egyptian films that Arabs watch, and because Egypt is one of the great Arab countries, and it has a great history.
3. The Gulf dialect: It is spoken in Saudi Arabia, the Emirates, Qatar, Kuwait and Oman.
4. The Moroccan dialect: It is spoken in Morocco, Tunisia, Algeria, Libya, This dialect may be difficult to understand for Arabs in the Arab East, but it is a lovely and pleasant accent when speaking.
5. The Iraqi dialect: It is spoken in Iraq, and it is close to the dialects of neighboring countries (the Levantine dialect and the Gulf dialect), and is widely understood by both.
In short: I advise you to learn the the standard Arabic, because all Arabs understand it, so you can communicate what you want through it, and they also can communicate to you what they want in formal language. Then you can learn the dialect spoken by the people you most expect to see.