For set-in sleeves, I sew the shoulders first - this is often necessary anyway, as there is a neckband or collar or hood to be put on. Then I find the mid-point of the sleeve and attach that at the point where the shoulder seam ends, then sew down towards the underarm; then attach the other half of the sleeve top, stitching down to the underarm. If I have enough yarn to keep stitching, I continue down to join the sides, and join the sleeves. Otherwise I join in a new stitching thread at the underarm to sew the sleeve and side seams, using mattress stitch.
Only once did I ever sew the sleeve seams first and it was awkward.
Stitching down the sleeve seam from underarm to cuff, and down the side seam, seems easier to me; it all seems to come together better and sit more nicely.
For raglan sleeves, the raglan seams are stitched first. Bands or whatever is happening at the neck usually come after that. Then the sleeve seams and side seams come last.