I live in Denver, Colorado in the summer and Naples, FL in the winter. I will offer several suggestions regarding a home gym. MY neurologists are and my personal doctors are all in agreement that some equipment SHOULD NOT be used by Parkinson’s Patents. One is a treadmill. Everyone is concerned that because it is in continuous motion, it is very dangerous for PK patients because should you fall, it is very easy to get injured. Walking is great with assistance, but, of course, dangerous if alone. The second piece of equipment is a stationary upright bicycle. Your feet are in line with your hips and falling is easy. I have been instructed to use an recumbent elliptical machine. It is more expensive than a bicycle, but it is doubtful that you would fall because you will be on a seat with your legs in front of you.
I have a TRX. This is an excellent and rather inexpensive piece of equipment. There are many exercises that you can do without assistance and you can get a full body workout. I also have a small foam balance pad for physical therapy measuring about 2″ x 15 x13″. There are many balancing exercises and stepping exercises that you can do either alone or with assistance. Another excellent piece of equipment is a jump rope. I also use some light weights up to about 25 pounds for numerous balance enhancing exercises.
This is a start and I hope it helps.