Thanks for the compliments Mark, it's good to have another vocal member on the forum, and I'm sure everyone here will give you sound advice.
Stretch, stretch, stretch after each session, even if the whole group isn't doing it and appear to just get up and leave, give yourself a good few minutes to squeeze all the lactic acid out of your muscles, that's where the ache comes from the next day.
I found that a drink with a tea-spoon of Creatine helped greatly even an hour after training, but I was doing that daily at the time anyway, so I'm not sure about just binging on it after a class, look it up if ya want a quick easy fix.
Something as simple as doing your sport less often, and then slowly building up intensity and frequency will give time for injuries to heal and prevent them becoming worse. You'll find your body adapts well after only a few weeks of training. As your technique improves, you'll also find that you will be straining less and less often putting imaginative angles of strain on your lower back and such.
Your instructor should also be able to help, and possibly will include more stretches as Rob mentioned in his instruction.
Creatine and other suppliments can be very useful. Protein will aid muscle recovery. Ibuprofen, rest and ice will all reduce swelling. (Don't anybody train under the influence of pain killers, drugs or alcohol. Just incase any dumb people were reading).
Obviously, if anything starts to seriously concern you, go and see your doctor.
Get some rest so that you are ready for your next class.