Well... I'm latino, and all the examples you mentioned really get on my nerves too...
Music is a terrific way to get into another language. Most of my early english knowledge came from songs.
But, you can find pretty much any type of music in any language nowadays. If you're interested in spanish, you don't necessarily need to listen to "latin music". There are terrific "spanish speaking" rock bands, hip hop, soul artists.
Also, keep in mind that spanish will be different in different cultures. It's not the same spoken in Spain, Mexico, Venezuela, Costa Rica, Colombia, Chile, Argentina, etc, etc, etc.
Supposedly, the purest latino spanish can be found in Colombia, so put on some Sofia Vergara videos and repeat after her....
(just kidding, she actually overemphasizes her latin-ness a little bit).