Body Pump or Crossfit are both good ways of getting into free weights movements with supervision.
If you are training for general fitness and injury prevention, range of movement, posture, flexibility and core strength are all very important. If you are new to strength training I would work to two strength sessions per week. Prioritise these, so even if you only do two sessions, do strength. Start with light weights and ensure you can do all the movements with a good range of motion and smooth movements.
Then add in conditioning, circuits, spin class, intervals on the rower, etc.
You will get better results training 4 or 5 days a week, eating well, and resting/stretching, than you will flaying yourself 6 days a week from the get-go. As others have said, mixing things around every 4 weeks or so, and having a rest week, is very important.