Do you think it is better to go to every class, but do a lower intensity version of what everyone else is doing, or maybe do less sets - or instead try to do as much as possible, but not go every day? I find that if I go two days in a row with full effort, on the third day I am pretty much too sore to even move normally, let alone try to do warm ups and sparring. Is it better to go every day but take it easier, or go full throttle and then take a break? Especially since it is not like the gym where you can alternate which part of the body you are working out.
Also, just in general, what techniques are there for recovering from muscle soreness quicker? Actual recovery of normal use, not just pain relief.
Strength training or aerobics?
I only do interval training 2x a week, and that is enough to see meaningful cardiovascular benefits and benefits to my energy levels and stamina. It takes me 30 minutes 2x a week. Back when I was doing 3-4 hours of moderate intensity cardio plus another 3-4 hours a week of walking, I didn’t see any benefits to my cardiovascular system, energy levels or stamina.
To help with muscle soreness eating a fast acting protein both before and after exercise, plus sugar along with the protein after exercise. I know that my muscles sometimes get really sore when doing HIIT, but eating protein before the bout works to help keep it under control.
In general, recovery takes 48 hours. Light activity usually helps.
I don’t know how old you are, or what kind of shape you’re in, but from my experience: suck it up. Even when you’re sore, once your muscles get warmed up and moving, you can get through the workout just fine. After a few weeks, you’ll no longer experience this soreness from the majority of the workouts.
My experience is coming from 10 years of martial arts training 4 to 6 days per week - workouts that made me ache for days in the beginning pale in comparisson to workouts that don’t make me sore now.
The one condition being to be aware of the difference between muscle pain from DOMS or lactic acid, and the pain from impending injury.
Go to all the classes, and do what you can. You will surprise yourself.
I’m 38, fairly out of shape, doing Brazilian jiu jitsu which is for all intents just wrestling, preceded by a very high intensity warmup. I could suck up the feeling of soreness, I’m not afraid of pain, I’m more worried about the temporary weakness, because if I’m too weak to fight effectively that ruins it for my sparring partner.
I agree with Chilliwack. Push through it. Your body will acclimate to the stress you’re putting on it and your ability to recover will improve over time. I’m pretty sure you’ll recognize the difference between a real injury and general soreness. Ice and take anti-inflamatories for the injuries. Take time off to heal if they are particularly bad and do some other form of exercise that avoids the injured area. Swimming often helps me recover from most injuries and it’s still a good workout.
Your temporary weakness is mostly in your head. Even if you are putting out 10% less than you would without the soreness, you’re still getting benefit from the workout and so is your practice opponent. Keep at it.
Why didn’t you tell us it was BJJ? I was picturing you huffing and puffing through some “body pump” class.
Yes, push through it. Especially considering that a HUGE part of the fight is conditioning, endurance, and the ability to dig deeper than the other guy late in the fight.
You owe it to your sparring partner to give it your all. You can breathe after the round is over. It’s only 1-2 minutes, right? 
Every time you feel gassed, go max effort for 5-10 seconds. You will be surprised what your body can do.
Most likely the biggest risk to your fitness plan is that your enthusiasm will fizzle out and you will quit. So the effect of the workout on your brain is more important than the effect on your body – as long as you avoid physical injury.
So I would go every day and do a less intense version of what everyone else is doing. The main priority should be to go consistently and do some kind of workout. Over time you are free to dial up the intensity.