- Modern Standard Arabic (MSA) is the most popular with foreign students. This is a modernized version of the litterrary Arabic. It is used throughout the Arabic world for newspapers and television. The trouble is that nobody speaks it outside of books and medias. People speak in colloquial Arabic. Educated Arabs will know it, but you'd probably end up speaking English or French with them.
- Literary Arabic (Fossha) is the language used in the Quran, the holy book of Muslims. This language is not spoken as it sounds a bit as Old English "Thou Art in a Shoppe". It is the most difficult of the three brands of Arabic to be learned. Unless you are a Muslim or a scholar, you will probably never study littterary Arabic.
- Colloquial Arabic is the spoken language. It changes from country to country, although for example you can learn the Levantine dialect understood in Lebanon, Syria, Jordan and Palestine. These dialects are almost exclusively spoken, people using Modern Standard Arabic when writing.
A lot of Egyptian dialect is derived from classical Arabic- Fossha e.g the word for car in Fossha/MSA is 'sayyarah' but in Egyptian dialect they say 'arabiyyah' which actually means 'cart' in Fossha/MSA.
Never learn the local dialect first. It's not a priority, especially for a short stay. You will pick it up on the street when living in Egypt but if you speak MSA to anyone they will understand what you are saying even if they can't reply back in MSA.
And Allah Knows Best