In terms of accustoming the body to lifting weights on regular basis, leading to improvements in strength and overall composition, in the initial interim, concentrate upon executing compound movements (those that use more than one muscle group).
Examples of compound movements include the squat, chest press, shoulder press, lat pull-down and deadlifts, using a weight that represents 70-80% of your one rep max.
As for your request for recommendations over working opposing muscle groups, within a session, the muscles should ideally be worked antagonistically. For example, you should perform the following: chest/back, biceps/triceps, shoulders/legs.
After compound movements (which should always be performed before cardio), I'd consider the following isolation exercises for the respective muscle groups, seeking to perform 2 sets of 8-12 reps. In order to obtain the greatest gain, concentrate upon slowly returning the weight to the starting position, since the eccentric (lowering) phase is where muscle building takes place. Granted, it'll hurt, but you'll benefit in the longer term.
Chest (also works the shoulders):
Flat bench flye
Incline bench flye
Cable flye
Incline dumbbell press
Back:
Bent over barbell row
Single arm row
Rear cross-cable flye
Arms:
Barbell curl
Dumbell curl
Cable tricep pushdown (as the elbows lock out at the end of the movement, ensure that the triceps fully contract before relaxing).
Dumbell tricep kick back (ensure that the weight is returned to the starting position in a controlled manner, with the elbows flush to the ribs).
Shoulders:
Upright barbell Row
Seated dumbbell press
Lateral dumbbell raise (don't lift the extended weight beyond 90 degrees)
Cable machine rotator cuff.
Legs:
Thigh extension
Hamstring curl
Adductor
Adductor
Calf Raise (While lowering the weight, ensure that the stretch is felt throughout the calf before contracting the muscle).
