So would your advice to someone wishing to learn Arabic (for the purposes of understanding / being understood by as wide of an area as possible) to learn Egyptian Arabic or to learn classical Arabic?
Because of satellite television, I would say classical - everyone will understand you, and although you will sound formal in your speech, you will also be able to read and write.
However, you will have difficulty understanding the dialect of the person you are speaking to. And if you have a dialect that you should understand, I would say it should be Gulf Arabic (Saudi Arabia, Kuwait, Qatar, Oman, UAE and of course my own Bahrain).
Economic (thriving free markets, not just oil-funded governments) and military activity in the Arab world is concentrated in the gulf, so unless you are trying to be a tourist (Egypt), the real value is in Gulf Arabic. Note that most Arabic teachers are Egyptian or from the Levant, and will try and persuade you otherwise ;)