In general there is a fine line between the two. I think of Ballroom as oriented toward performance and Social dance as oriented toward personal enjoyment.
It depends on the dance. Most of the time you don't. Often there is a beginner lesson prior to the dance where you can meet other people new to dance or just new to the scene. Also, you should never hesitate to ask someone to dance (whether you're a guy or a girl).
It's a good idea to have a pair of shoes designated as your dance shoes just out of consideration for the floors on which you dance. Many dance floors have surfaces that are specially made for shoes with leather soles. However, if you can't make that investment, it shouldn't stop you from dancing. Just wear shoes you're comfortable turning and sliding around in that won't give you blisters.
Also bring a towel to wipe the sweat from your brow. Yeah, I wrote "sweat"! :)
Bottled water is always a great idea, or at least a bottle to put water in so that you don't have to run back and forth to the water fountain.
Lastly, make sure that you have some deoderant, hair clips, breath mints, and other stuff like that so that you don't scare away any potential partners.