I think for weight training, you should really focus on creating a routine and I'd try to stay away from machines as much as possible. For abs, I'd try to see if there is a ball available that you could do and use that to do crunches on versus using the machine.
Here is a page that could give you some ideas of workouts:
http://www.stumptuous.com/category/t.../workout_ideas
One of the things to remember with weight training is our body has large muscles and small muscles. Often the small muscles get worked while working the large muscles. Also, if you are using dumbbells or anything else that requires stability, then your core is getting worked so the need to directly work your abs is lessened. If there is a bosu available, you could also do some exercises on that and that would work your balance/core as well. (EG doing lunges with one foot on the bosu, doing bicep curls while standing on the bosu, etc).
For legs, lunges and squats are 2 of the best workouts for the legs. For the upper arms, pushups and pullups are the best workouts for the upper body. If your gym has an assisted pullup machine, that can help you work on your pullups. Changing hand position with pullups works different muscles.