This would be a 1st inversion, since E is first chord tone in Cmajor that comes after C. A 2nd inversion would yield a G as root. If the chord was, say a Cmaj7 (therefor there are now 4 chord tones), you could do a 3rd inversion which would yield a B as root.
As for whether you have to learn ALL the inversions of EVERY chord... well if you ever do that I will bow to your skills and you will be a Certified Virtuouso. Seriously though, learning inversions of chords is definately a good idea if your into jazz, but for a standard rock player it isn't necessary to have them memerized. However knowing how inversions work and knowing how to make them work for you is a good idea.
Note: I'm not entirely sure that that is how inversions are named (what I said in paragraph two). Could someone confirm?