According to the ACE Personal Training Manual (American Council on Exercise (2003). ACE Personal Trainer Manual (3rd ed.). San Diego, CA: American Council on Exercise.):
Because the muscle rebuilding process typically requires about 48 hours, strength workouts should be should be scheduled on an every-other-day basis. Clients who prefer to train more frequently should avoid working the same muscles groups on consecutive days.
The ASCM (see "Frequency") recommends weight training 3 days per week if doing a total-body workout and 4 days per week if doing a split routine (different muscles on different days, to work each muscle group twice a week).
So, if you know you want to weight train 3 times per week, I would apply this information by recommending you leave 48 hours between each workout and do a full body workout every time. If you work different muscles groups during each of your three workouts, you may not end up meeting the recommendation to hit each muscle group 2-3 times per week.
For completeness, the ACE manual also mentions that more stressful training sessions may require a longer recovery period. In these cases, a split routine (targeting different muscle groups on different days) could be justified.