When applying effects copy the vocal track and apply different effects to the different copies to avoid them muddying up the mix. Chorus effects always sound good on vocals.
Composite tracking reduces the amount of harmonic distortion and makes the sound a lot cleaner. To achieve it in a DAW you make two copies of your vocal track, apply equalizers so that the top range of frequencies is up on one track and the mid and low on others, and finally mix them back together.