My two cents:

Basic Wkout shirt NOT Cycling. - I would simply wear a wicking jersey and I use sleeveless as it is so hot.
I save Cycling jerseys for cycling as I figure easier to wash / dry others cheap wk out ones.

Basic wk out shorts with like leggings /under armor underneath - Seat is padded - no need for cycling shorts. This way you can go wk out after, and easier to wash/dry etc.

Water-or gatorade - you will need it.

Mid size towel - you will sweat alot.

Wipes - if gym does not have them - not a bad idea to wipe handlebars for germs/winter.

Extra shirt - I sweat alot so bring extra shirt for after.

MTB shoes preferred - this way you can walk easier and not slip when stretching etc.

Try different instructors to see who you like.

Ignore instructor if they make you do some silly wk out on bike or try to make you stand too long.
Create your own intervals / zones / recovery if they are clueless.

HRM - till you figure out your intensities etc.