All good contributions.
I'd emphasize the need to spend time with mic selection (a great mic for one person's voice isn't necessarily a great mic for the next person), placement, and distance. Face into a corner, face out of a corner. Put the mic here, put it there, have the singer work closer and more distant.
Record all the experiments. You can't really tell what you're getting as you lay it down; you have to hear it back.
Oh yeah, and run all the experiments with EQ flat; don't cut or boost ANYthing.
One of the experiments will yield something you like better than the others. Then spend any amount of time necessary in getting a good perFORMance. Players, especially at the home recordist level, pour tons of effort, time, and angst into getting great instrumental tracks, forgetting that to most listeners, all that is just a vague pillow for the lead vocal.
Get multiple takes if necessary, wait for a good one, and know when it's gotten as good as it gets. If the best you can get is excessively pitchy, you might have to punch in a verse or a line at a time. Not ideal, but it can be done. Pitch correction software (Antares Auto-Tune) is easily overused, but it CAN quite invisibly fix intractable pitch problems. Do NOT overcorrect!
I never compress while tracking unless I have a completely uncontrollable singer who canNOT give me his/her loudest level in the setup. Then I'll put some kind of soft-knee limiting on it, just to keep the voice from burying a meter and clipping.
As everyone says, the more attention you pay to the fundamentals – the mic, the placement, and the performance – the less trouble you'll have in the production phase.
IF I have to compress in the mix, unless I'm looking for an obviously artificial push and pump in the sound, I use the gentlest ratio and the mildest setting I can get away with. Usually I'm trying to solve a problem – inaudibility in one area, overs in another. If those problems are serious enough, it's time for some waveform editing on the individual track. Otherwise, a touch of compression can help the track lay better - remain intelligible without overpowering.
Bear in mind that, as producers and engineers, we often try to compress and eq to solve arrangement problems – where there's too much going on in instrumental tracks, or frequency masking from parts which have no business stomping all over the vocal range. There's only so much you can do.
If you're also the arranger and the band, listen for stuff that gets in the way of the vocal. May be the greatest guitar part you ever played, and if it fights with the vocal...better move the guitar part.
If I compress, I do that first in the signal chain.
Next, EQ. And darn LITTLE EQ; as everyone says, always better to cut than to boost frequencies. In busy material with active bass lines, it can be useful to peel most of the low end off the vocal (under 200, say). Bear in mind that every mic known to man has a "presence" rise at some frequency point, which is what gives it its character. If you've done a good job of matching mic to singer, you'll already have a pleasing vocal EQ by virtue of the mic's own response.
But you CAN give it a slight rise somewhere in the upper mids, a fairly narrow and slight boost, to aid presence and intelligibility, and to fit the vocal in among the EQ stack of everything else going on. (If it's fighting with an instrumental part, you can notch the guitar a little at the same freq.)
But all these things take subtle adjustment. Too much EQ sounds artificial and generally ends up being tiring to the ear.
(Unless you're going for a special effect of some sort, in which case...do what thou wilt.)
I've come to utterly despise most effects on vocals...doubling, chorusing, phasing, flanging, big ambient delays, blah blah. Rockabilly slapback delay is a thing unto itself, and can certainly be effective, but also threatens to sound trite and hackeneyed. If it HAS to have it, go ahead...just recognize your track will sound like a quote of every other time that's been done.
Ambient delays...I dunno. Big power ballads from the 80s, 60s-70s experimentation, it's all been done. It can add a sense of dimension, and shouldn't necessarily be avoided at ALL costs...but should only be brought in when the basics aren't working.
Which leaves reverb, and that's the key to a great vocal sound to me. VERY few vocal tracks are truly completely dry; even apparently very plain tracks generally have some kind of reverberant halo around them.
But there's an art to making the reverb fit the vocal in the tune. Any modern reverb has a whole slew of parameters to adjust, and it'll pay you to learn what they all do. In particular, pay attention to early reflections, crossover points (if it's a multi-band reverb), and whatever functions affect the apparent brightness of the 'verb.
A reverb that kicks in too immediately (too many early reflections) can muddy up the vocal; a reverb too dark or too bright won't work either. There's considerably more to it than just how long the tail is, and how "big" the apparent room is.
Can't tell you WHAT to do - just play with every parameter you've got, from mild to extreme settings, till you understand what they do and how they interact. You don't have to pour the reverb on...sometimes a short subtle ambience around a vocal, which just seems to move into a slightly bigger, airier room, will give it sparkle and life.
My default effect order, if I'm chaining them (in real world or virtual) is dynamics/compression -> EQ -> delay or other candy, if needed -> reverb.
But I try to get everything I need with minimal comp and EQ, then dial in a magic 'verb for the song, beFORE I consider any other candy.
Basics, basics, basics...