Every singer is different, mic that sounds good on one, dudu on another. The mic you choose depends on how your monitors are set up, or visaversa. Wedge in front=cardioid, double wedge=hypercardioid, with sidefills too=more difficult, IEM=less difficult. A hypercard will feedback on a wedge in front, a card will feedback on a double wedge.
The size of the stage and height of the ceiling are important too.
Compression can wreak havoc on stage, better if it's only for the FOH, fast attack and fast release, slow release will bring you some nasty problems.
Monitors are rung out to avoid feedback, FOH is calibrated to even out anomolies in the venue, it's better that you have two situations of eq.
Do you need lush or tight and dry? The whole chain can be chosen on these factors. Lush=tubes, tight=solid state, even though there are exceptions to this.
With any combination, the mic technique of the performer is crucial. I can't tell you how many good singers and wind players don't have the slightest idea. Don't cup the mic, this turns it into an omni, don't leave the mic close in front of your head or body for too long, it picks up everything behind it, wedges. Watch some Marvin Gaye vids.
The most influential part of the chain is the mic, everything else will follow suit.
Rock? Dynamics are usually better for this, hard loud music. Condensers for any thing else.
A Lexicon, a TC 2290 delay (tap tempo) and an Eventide harmonizer (thickening doubling) come in handy but sparingly and FOH only