You don't have to learn them all at once, but over time you will learn a lot of them. Some you may forget and have to lookup, others are used all of the time, so you won't forget them.

As a baseline, I think you should know all of the major and minor chords. From there, you can easily derive suspended, 7th, 6th, etc. variations. Then you have the barre shapes - you memorize 2 shapes and then you need to know the bass strings to know what chord they represent on which fret. For instance, the bass E string on the 3rd fret is a G. Play a barre E shape on the third fret, and you are playing a G chord.

My personal feeling is that you shouldn't just learn all of this stuff for wrote - it won't stick. Learn this stuff in the context of songs - it will stick much better since you'll have context. Get song books of music you like that shows the chords and play along.

Hope that helps.