look at shure.com. akg.com and atus.com. They have charts dividend into 3 categories: Gold, siver and Bronze suggestions for every set-up.
I recommend you AT4050. I used 3 of them everyday.

Maybe not the "best", but one of my favorite general mics:

Shure SM-7B.

Bowisc

You might mention what PRICE range you're looking in.
I mean, if I recommended a U-47 would that be useful?

Basically I don;t hink it's fruitful to think about it in terms of genres.
Some rock singers on some kinds of tracks sound great through that aforementioned U-47 and others sound too hi-fi and do better on an SM-7 (or even an SM-57)(ugh)

It realy comes down to the best mic for the SINGER rather than for the "style".
Most records, i think you'll find, were recorded with the vocals on big diaphragm condensor mics, irrespective of musical style.
the exceptions get mentioned because they ARE exceptions.

If you want to purchase a mic in anticipation of these vocal styles, I would say the you have the cart in fornt of the horse.

If it were me, I would find a store with a large selection, and arrange some demo time, or locate a rental house to rent an assortment.

Mics are like eyeglass. You can't use the same formula on everyone, reguardless of style.