Changing from punches to the press really increased my quality....big time. However much of what I was doing at the time involved thicker and/or stacked leather projects. My ability to maintain hole alignment on multiple stacked parts was simply horrible. So much better results by drilling after contact cement assembly.
As others have already mentioned, be sure to keep the item on a level plane, or wonky results may follow. I've had my fair share of projects that look great on one side, but the other side has looked like a "sight challenged" person used power tools for the very first time.
Many suggest using a needle or awl tip. With drill running, or not. I've only used a drill bit, running. Don't know the size, but it is the smallest bit I've ever seen. It does remove material, so keep that in mind if thread is thin. And I also have been using a rather thick, heavily waxed thread, that has needed an enlarged hole. At least, that is, in order to save my sanity, needle breakage, or finger and palm damage.
Sent from my mind....using Tap-a-Thought. (tm)n