Just to be clear from the start: there is not one single aspect of strength training that will suit everybody.
Free weights and dumbbells, as well as machines, will help you gain strength, the effects varying by person. Also, remember that other options exist, such as elastic bands or lifting one’s weight.
Strenght training options
The choice between free weights and machines is ultimately up to you, and should be based on training level, personal preference, goals, and, logically, the availability of either option.
Free weights are versatile and inexpensive, simulate everyday situations that require lifting weight, and generally promote balance and body stability. Generally speaking, weights are safe when approached with the right technique, although this can take some time.
Machines can be just as effective when it comes to increasing strength as long as you use them according to your body size, and your arms and legs can move naturally. Machines are usually safe, easy to use, and a lot more fun than they appear to be.
In conclusion, you should decide on the system you like best, the one that matches your lifestyle and provides the most benefits over time. Try to work out main muscle groups at least twice a week, leaving a day to recover in between sessions.
Whatever you choose, never forget that the key to an effective strength training is technique, not training style. Injury will force you not only to interrupt your training, but could also be very harmful.