[elliskit]

I agree that there is much debate on this subject, but:
If there is no manual manipulation of the clubface, the only plane that produces no arc is vertical. That is not a very natural "feel" for me to try to swing on a vertical plane. I have MUCH left to learn, but I can testify that after about a year of trying straight back - straight through with negative results, my distance control has dramatically improved with merely swinging the putter on an angled plane, tracing a straight plane line with no manual clubface manipulation. This motion makes an arc when you look straight down at the putter head from above. It "feels" very natural to me. Like Geoff says, pull the putter back far enough so that when you let it fall by gravity, it produces the right impact speed. You do not have to think at all during the stroke.