I agree with MTS comment that you do not need much to start with. Whether you need more or not will depend on your focus: which part of the theory are you interested in?

Personally I would reccomend Serre's Complex Semisimple Lie Algebras as a must since you most likely will end up fighting with Serre's relations.

Also, classic books on Hopf algebras are not to be forgotten; here the choice is between Abe and Sweedler, if I remember correctly the title is "hopf algebras" in both cases.

As for the three books about which MTS does not add comments let me say something:

Joseph's book requires a solid background on Lie algebras and their reps, otherwise it's almost impossible to understand its directions. With this background it's a very intriguing, though demanding, reading.

Brown-Goodearl is a great book to start with. It's built from lecture notes of a course and therefore "learning oriented". It's much oriented towards the more algebraic part of the theory. I would reccomend McConnell-Robson book on Noncommutative Noetherian Rings at hand...

Lusztig's book requires feeling at ease with various categorical issues: definitely not a first reading. It is also uite narrowly focused on some specific aspects. I would not put it in any list: if that is your direction at some point younwill be forced into it.

I do not know about Jantzen's book.