My two cents:
It starts with the performance: You won't get an intimate sound, if the singer is not close to the microphone - try to have him or her imagine the intimate space when singing. Personally I wan't to be able to hear every breath, every lip sound - well maybe not hear, but sense...
I normally try to be very sparse with effects - gentle, serial or parallel compression, and a reverb, that's gotta be spot on. I my opinion that is the hardest part.
If you happen to have a well sounding room you could try and experiment with a room mic.
You can use basicly any well sounding microfone, but be careful with condensers if the singer has a loud voice - not all condensers can cope with the power of a really loud voice close up.
Try and use what you have and experiment - actually my own voice sounds really good in a SM58 - not the beta - but the oldest, cheapest mic out there... 🙂