I tell you some suggestion
You can learn a dialect while learning standard Arabic, because standard Arabic is really important when reading news and books, and when communicating with people who doesn't understand your Arabic dialect. So when you learn something new in standard Arabic just find it's equivalent in the dialect you want to learn, it will be easy as they are quiet similar
About choosing the dialect, Egyptian is widely understood among the Arab world, Lebanese we Egyptian can understand it but don't know if all the other countries understand it well, so you can choose what sounds nice to your ears when you hear it.
Hesham