Hi Lena! It sounds like you're off to a great start!
When they're first starting, most people complete all three sets of one exercise before moving on to the next exercise. BUT ... they rest between the sets. So (using your example), you'd do A - rest 30 to 60 seconds - A - rest - A - rest. Then B - rest - B - rest - B - rest. Etc.
The reason you couldn't do as many reps with the AAA scheme was that you weren't resting between sets, if I'm reading you correctly.
The ABC scheme is circuit training, another good way to train. With it, you DON'T rest between the ABC sets because the A muscles are resting while you're doing B and C. You rest when the entire circuit is finished, like you indicated.
The benefits of circuit training are 1. speed, and 2. it keeps your heart rate elevated because you're not resting until the end of the circuit and so you burn a few more calories.
As for the arms and legs, they're usually done at the same time. However, if you're doing an exercise that you want to alternate right and left, you do that within the set, not as separate sets. Let's say you want to do alternating bicep curls. You'd curl R - L - R - L - R - L - R etc until you did the correct number of reps for each arm. Same thing with something like alternating lunges for legs.
Hope this makes sense - keep asking questions!
Weight Lifting Reps/Sets Sequence
I'd probably do a set on the left and then do a set on the right, without a break. But there isn't any right answer - which is true of almost everything in the gym!
