For resistance exercise: You don't need to pump iron in a gym to do resistance exercise. Of course, if you want to go to the gym, I wouldn't discourage you. But if you prefer to do it at home, you can. I recommend exercise tubing if you're looking for a simple but effective way to do resistance exercise at home. Exercise tubing is inexpensive and versatile (you can do lots of very different exercises with them) and they are a great way to get started with resistance exercise. You can start with a set of four for about $20. They come in colors to denote the tension. If you order them, make sure to order the strap that allows you to attach the tube to a door, and if you want to work your legs, ask for leg straps. Here are some vendors that sell them:

Many of the problems that older people have are due to weaknesses caused by inactivity rather than a chronic disease, and a physical training program can have a wide variety of benefits that aren’t just physical. Older patients may socialize more frequently, take care of themselves, get out in the community, and experience more thanks to improved confidence!
Since accidental falls are a significant source of injury for many older adults, incorporating balance exercises in your exercise regimen is essential. Doing balance exercises, such as the ones described here, or an activity such as tai chi or yoga, makes it easier to walk on uneven surfaces without losing balance. You can do these balance exercises every day, several times a day — even when you’re standing in line at the bank or the grocery store.