I find writing vocals first to be the most challenging and most rewarding way;
A set of lyrics on a page suddenly becomes a tune. You play the tune using any keyboard voice at random, then set about working a drum pattern around it. Spaces open up for bridges, cadenzas and codas, and it's time to work out some basic harmonies.
This is always fun, as the voice line can suggest many harmonic variations, and you can simply throw one off-the-wall chord in there, and the implied harmonies all change.
Adding bass becomes even more fun, as you can alter all the harmonic expectations - but it starts to become a precision art at this point.
Now comes the colouring in - turning the harmonies into rhythm parts or simple lines, intertwining...
All the time, the drum track and bass need simultaneous tweaks to maintain the rhytmic, harmonic and (in the case of bass) melodic sense.
Then I add rhythm guitars and vocals. Often at this stage, a rhythm guitar part can colour a vocal line and vice versa, or a keyboard part will suddenly jump out as being more important.
Next vocal harmonies.
Sometimes I have completely stripped out harmony layers just to get the vocal harmonies I wanted. It's all sacrifice for the greater good!
Lastly, guitar or keyboard leads. These require little effort - the hard work is all in building up the overall picture that you're trying to paint. Get the cake right and it practically ices itself.
That's my "normal" approach, anyway... needless to say, I do it differently each time I write as it's more exciting that way - I never know what I'm going to come out of the studio with