One major wipeout where you skitter down the road on your palms, and you won't ride around the corner without gloves again! At least I don't!
I can't imagine they would put you on clipless pedals for a class targeted at newbies, but call and ask. I would wait on those until you have been able to give some thought to the styles available. As an aside, I found my spd clipless double sided pedals to be very easy to adapt to- all the horror stories scared me.
So my list would be: helmet, gloves, and shorts if the rides are likely to be over 8-10 miles. Personally, I like to have cycling shorts on every time I ride, but I know some people can do 20+ comfortably first.
I have found that special bike gear really does make a difference- I love riding in jerseys because they are really cut to maximize comfort when cycling. But they cost a mint and I would wait to phase them in over time.