This is an interesting post, so I'm reviving it.
Going back to fundamentals, I would say that my "chain" first consisted of understanding how the space sounds when you sing. Is it dead and if it's alive, are there any sound artifacts that might come through in the recording. Does added reverb work to treat a dead vocal? Or should I look for a better space to record the vocal track?
Second, I think about the voice itself and what kind of mic is the best match. I constantly struggle with harsh vocals. So sometimes a Shure SM7b is my first choice. On the other hand, sometimes that mic is not roomy or full enough. It's eliminates most of the room sound, but that's not always a positive.
Third, I rely on a pop filter and placing the singer (me) at the right distance. I also think about the words I'm about to sing to determine which might cause plosives or sibilance. Then I remind myself: "No sibilance please. Your Logic DeEsser sucks."
And put down the coffee, It causes you to sound sibilant.
Fourth, I plug into a Great River Me1nv routed to an Apogee Duet. The processing is usually simple. EQ, compression, reverb. I use primarily Logic native plugins to keep things simple. I also have some Waves vocal plugins (mostly Renaissance). They tend to be simple with few controls and sometimes I don't feel like digging under the hood. If I use the logic compressor, I sit there all day rotating the attack and release knobs
Lately, I've been playing around with parallel compression to get more volume out of the vocal. Here, I'm just bussing the vocal to another Logic compressor. I've also been fooling around with multi band compression on the vocal track to address my harshness problems. The idea being to isolate the offending region (3.5-6k?) ad gradually add compression.