One of the neatest finishes to seams in a shirt is the flat-fell seam.  I learned this technique many years ago when sewing pj's for my siblings and I.  Step 1:  Place the pieces wrong sides together and sew the 5/8" seam.  Step 2:  Trim one of the seam allowances (s.a.) to 1/4".  Step 3:  Spread the pieces flat and press the s.a. over the trimmed s.a.  Step 4: Turn the raw edge of the s.a. under about 1/4" and stitch close to the fold.