I’ve found that a simple set of resistance bands can work well for my clients. With bands we can adjust the resistance to almost any level we want by widening or narrowing the base of support, etc. Bands seem work well for teaching my clients proper muscle control throughout a paticular range of motion. The downside is that on some exercises like a chest fly, the bands can prove a little difficult to mangage and sometimes they can pinch the skin. Overall I think for in-home training bands are cheap, efficient, and reliable.
I like free weights for most clients, especially those just beginning a strength training program. With dumbells and barbells you can teach your client to execute safe and effective movements. While the many machines on the market offer a variety of resistance exercises, the reality is that some of them don’t correctly fit your client.