I said that this depends on your English learning goals, but if you don't have a goal the best choice is to start with "casual English", but in both cases if you learn the two is better.
If you didn't see the previous article, I highly recommend that you go to the article here Everyday English or Formal English and read it first.
Well, in this article we are going to talk about the differences between Casual English and Formal English.
The first difference between the two, is the use of each of them. Formal English is being used in Academic situations, for example if you write an academic letter, you should not use slangs and informal English!!!
A second use of formal English is with people you don't know very well, or older than you, but this one is going to disappear step by step.
Casual English is used everywhere, for example if you have some friends, you won't use formal English when taking with them. Also when you talk to your parents...etc
Casual English is more used than formal English. If you speak formal English in no Academic situations, people will immediately see you as a strange person. In the other hand, if you use casual English in an academic situation, they will think that you are impolite, so be very careful where to use each one!!!
In formal English, you should only use words you find in the dictionary, you should use correct grammar but in casual English, you can use Slangs, idioms, incorrect grammar...
Another thing is that formal English is used especially when writing but everyday English is used when speaking. In fact native speakers know when using each one without thinking, they think that this is a formal situation or not, they instantly use the right type.
If you live in the United stated, you will know everything about this topic. Remember: listening is the key to everything is your English learning!
Slangs are new words, these words have been added to the spoken language but if you look in a dictionary you won't find them!
Idioms are strange expression where you can understand each word, but you can't understand the meaning if you didn't know it before. For example: if I say that I "feel blue", I know you understand the word to feel, and blue (color) but to feel blue??? well, it means to feel sad!!
You can know more about English idioms at American Expressions
If I say: He is a couch potato, it means that he is a lazy person.
For the grammar, Americans usually don't use "that" in phrases like: The car "that" you bought. They say: the car you bought...
Well I think this is enough for to today, you can know share some idioms and slangs in the comments. I also encourage you to subscribe to the RSS feeds.