Ha! I'm pretty short (5' 1 1/2"), and I do no such "bouncing about" and all that when I teach classes. I refuse to be Suzy Aerobics Bunny in class. I think that's why my classes end up being so much fun.
P.S. I hate going fast.
Look for the abs and stetch classes, core classes (abs, back and stretch sometimes), stretch classes, and pilates classes- especially the pilates classes. If you want to strengthen the core, pilates is wonderful for you. I've gotten a bit stronger with some of the pilates classes, and my core classes are great- I make them about as hard as anyone can take, and then some. I usually do about 15 different ab exercises in my classes for abs that run about half an hour, nonstop. I don't allow people to rest between transitions from one ab exercise to another. All the ab groups get repetitively taxed for the full 30 minutes- internal and external obliques, rectus abdominus, and transverse abdominals. Look for classes where they specifically name all the exercises that name these abs.
My pilates classes are basic, but they do work to strengthen abs, back, and shoulders, as well as emphasize deeper breathing. See if your club offers a beginners pilates or intro to pilates class. You can ease yourself into the regular pilates classes. If you have the money, consider taking a few pilates reformer training sessions instead. Reformer training will make you much stronger in the core than pilates matwork.
I do think it's always a good idea to take other aerobics based classes. It's not always about cycling- and if you cross train, you'll only become more efficient aerobically. So look for other aerobics based classes. It doesn't have to be step- you can do kickboxing, boot camp, cardio circuit, spinning, treading, etc. Look at what your club offers, then audit the class- if it looks good, then try it out. Show up 15 min early and when the instructor arrives, immediately tell them you're new. That way, they can keep an eye on you. A lot of beginners tend to gravitate towards the back- so I spend quite a bit of time targeting members in the BACK. Smart beginners that don't want to get pointed out stick to the front of my class.
As Eric said, ask after class if an instructor can take you through stuff you don't understand. Sometimes, we are running from one gym to another, but if we aren't, we also like to talk about our classes and moves and stuff. I sometimes even recommend videos I use to other class members too. Shoot, I got nothing to hide. And I want my students to do well in class.
Finally, if you're not having fun, find another class. People suffer in my class... yes, they do. But as hard as my classes are, they are also a lot of fun! We are either laughing at the music (aerobics music can be ridiculous), or they laugh at my warm ups (I hate hate HATE doing hi/lo and step, but it's the best way to warm up!), or I am usually mocking the gym or my boss (they sometimes say the dumbest things to me, and they are always worth repeating to the students in class for a good joke), or I'll call out on someone I know in class and do some good natured ribbing, or sometimes, I nickname people in class- I give funny nicknames to peope based on their personality, or if I switch moves and someone is slow to follow, I call them the "drama queen of the day". If someone shows up late, I call them "making an entrance". If some people seem to send lots of time talking to each other in class, I call them my "troublemakers". And nicknames tend to really work. They stick. When someone emails me (I give everyone my email so they can email me if they have something to say or ask), they'll use their nicknames I've given them. In spinning classes, I also give out cycling based prizes- I've been to so many cycling events, like races and crits and all, plus bike factories, plus I've picked up some cycling gear here and there, and they make great prizes. I'll usually talk about upcoming bike races in class and tell them when they'll be shown on television. Then the next class, I'll ask people a quiz question from the race. If someone answers, they win a prize. I just have so much cool schwag, and people usually like what I have, so they will watch the bike races. Then we'll run through a bike race in class. If the club has a television with a vcr or dvd, then we can also run through the featured race after we talk about the race and I've given out the prizes. Lots of fun.
Soooooo... that's how I run classes- I hope other instructors really try to get their students involved in the formats they teach, and I think those classes end up being more fun and informative and of course, since I'm a commando... very hard. But at least you get a lot out of them. Look for classes like that, and I think you'll be better off in the long run.