I use a multi point safety type center for 90% of my small to medium blanks. For turning pens between center I use a fixed 60 degree point center. I sometimes us a 3 or 4 prong drive center for large blanks, but normally switch to a face plate or chuck if it is too large for the multi point center.
I think machining the centers to fit the lathe makes more sense as then you could use in the tail stock as well as the head.