It's hard to say. Everything is individual. It depends on your goals, your experience level, your recovery ability etc.
Given from what you said, you are an absolute beginner. Your soreness the next day is to be expected. How did you feel the day after that?
I would probably do something similar to what your trainer had you do on day 1. Do 1 set of 12 each of 8-12 machines and do this on 3 nonconsecutive days. As you go along try doing an extra set on each exercise until you are doing 3 sets of each exercise. Along the way, try to learn the free weight equivalent of each machine and institute them into your program. I'm assuming that the exercises you were shown was a nice mix or upper and lower body exercises. If not make sure you have a balance there. As you add sets, you may want to keep the number of different machines/exercises down towards the 8.
Once you get up to this level, you will have a better understanding about how your body will react to resistance training and will then be better able to gauge whether or not a total body, upper/lower, or other split and which set/rep schemes are most suitable for you and your goals.
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