I've only done a few live drafts, but simple excel has worked great for me in the past.
I like that I'm able to customize it all I want and add columns for filtering and sorting.
Info that I usually have:drafted (check once drafted)
my rank
my position rank
player name
position
team
my position tier
my notes
ranks from different sites (and an average site rank)
Then I have filters for position and drafted.