I am not an OT or PT, and therefore cannot give you specific advice other than to hire a personal trainer/coach at the gym where you have the access. This is the safest and most productive method to learning to use the gym facilities.
I recently did just that. I hired a personal trainer for the minimum amount the gym would allow, which was 5 sessions. In those 5 sessions, I had the trainer give me a series of exercise routines tailored to my goals. She taught me HOW to use the machines without hurting myself. It was well worth the money to hire professional help.
Swimming is always a great way to exercise, too. If the gym has a pool, see if they have the exercise classes that are in the water. This might be very useful for your weak side.
Good luck with your exercise program. The most important part it to GET TO THE GYM and exercise!