Rowing machines and exercise bikes are both great choices for a home gym. They're affordable, easy to use, and take up very little space. They're also low-impact, making them suitable for people with joint issues.
However, we give a slight edge to rowing machines. They're a bit more affordable, have less chance of injury, and provide a more full-body workout than bikes do. They can also be much more fun since you're moving most of your body instead of just staying in one place.
At the end of the day, picking the right machine for your home gym is completely up to you and your needs.
If you'd like to take a look at different rowing machines before you decide, consider Aviron.