hi steve, and welcome to SF! glad you joined the program.
I have never trained just with bodyweight and because of this I am very skeptical of this program. I'm hoping that this is just not a fad and that I will really see some result after putting the time in.
rest assured mate, this is not fad at all! put in the time and effort, and i guarantee you results - or your money back! (shit, i can't promise that, cause this is free).
to answer your question:
pull-ups - palms facing away
chin-ups - palms facing you
neutrals - palms facing towards each other (obviously, you can't do neutrals on a normal pull-up bar)
as to which one is the best: i suppose it's a personal choice. for me, chins are the easiest and pull-ups the hardest, with neutrals sort of in between.
the purists will tell you that pull-ups is the only way to go (which i suppose is the correct approach). unfortunately, due to an injury, i can't do pull-ups, so i do the next best thing: neutrals. so again, personal choice and circumstances. but don't forget, whichever grip you use, you are still lifting your own bodyweight - not something everybody can do!
and remember, apart from working different muscles in the arms when using different grips, you are also using different shoulder and back muscles. each grip targets specific muscles in the shoulders and back as well - so that's why i think it's important to "mix it up" (using different grips) - especially on D1 & 2
go and create your own thread on the "workout logs" page and post your results - it's always nice to see fellow SF'ers progress and it serves as a great motivator!