I record my vocals on an AKG C-3000 which I've had forever. It's nothing fancy, but I think it sounds pretty good with vocals, as it seems to have a little bit of a mid-range bias, and this can be helpful in getting your vocals to sit right in the mix. The down side is, if you've got a singer with a lisp, or just a sort of "spitty" way of singing, the mic will exaggerate it.
The mic is plugged directly into the XLR input on my MOTU 828 mk II. I'd love to have a fancy, high-end recording strip for stuff like this some day, but for now, this does the job just fine. Very neutral sounding, so it gives you a good starting point.
Once I've recorded several takes, the first thing I do is to build a comp of the best bits from each take. This way, I'm starting with the best results possible. Now's also a good time to listen for mic bumps, mouse farts, or other unwanted sounds that need to be edited out.
The first item in my typical vocal channel is an EQ. The sole purpose of this EQ is to filter out the unneeded low frequencies. The reason it's first in my chain is that I want to get rid of them right away, so they don't effect the way the compressor works. Having an EQ cutting out the lows is really a good habit to get into for almost any channel (aside from bass and kicks, although even they can use a cut around 40Hz and below). It will clean up the low end in your mixes and free up all sorts of headroom in your mixes.
Next up, I have my compressor. Even though I have a LiquidMix, which has models of classic analog compressors, I actually prefer Logic's built-in compressor on my vocals. It's a very clean and neutral sounding compressor and really lets vocals come through clearly. If I need "character", I can always add it later. I tend to compress my vocals pretty heavily... a ratio between 6:1 to 10:1 with an aggressive amount of reduction and relatively fast attack. There really is no magical setting that will work for every voice. You just need to spend some time experimenting to find what works the best with your vocals.
I follow the compressor with another instance of EQ. Unlike the previous EQ which consisted of a heavy low-end cut, this one is aimed at boosting a couple of key areas. I'm putting it after the compressor because I want to exaggerate these frequencies in the already-compressed signal. I find this allows for more subtle results and a greater ability to fine-tune easily. My typical boosts are around 1500Hz - this is an area often associated with intelligibility of vocals, and can help fit a vocal "in" the mix instead of on top of it - and at 10k, which adds a little "air" and presence. Neither of these boosts are more than a couple db's a piece.
The second EQ is followed by Logic's Sample Delay plug in, which is designed to allow you to offset the left and right channels of a track at the sample level. When you delay one side versus the other, the result is a stereo "widening" effect. I think this makes the vocals sound a lot slicker and more professional, but it also helps the vocal fit in the mix better. It might not be right for every case, but give it a try and see if you like it.
Finally, I have to aux sends, 1 which goes to a reverb, and another that goes into a delay. I'll use different ones for different purposes, but I always keep my send levels pretty modest... about 20% or so. This helps give the vocals space, but without overwhelming them. Vocals are generally mixed pretty dry these days, so mess around and find what sounds right in the context of your song.
That's it. Pretty simple. How about you? What's your go-to effects chain for mixing vocals?