My general recommendations:
What is right for you may not be right for someone else. There are a lot of variables to consider. If you are already working out and prefer to buy individual pieces I would suggest you invest in a bench and dumbbells. You will be able to get the most for your money and work every part of your body. When you are ready you can buy a bar and plates.
If you are new to working out no matter what your age a universal piece will be easier to learn than dumbbells. If you like the idea of dumbbells perhaps you can find a trainer who will come to your house. You can also buy a book or two but proper form is essential.
You will want a mat so you can stretch and do abdominal work. You don't need a piece of equipment unless you really want one. I am familiar with many pieces of abdominal equipment. They have their pros and cons. If you can get down on the floor, in my opinion, you don't need any kind of machine.
You can add some resistance bands for variety if you like and a stability ball. Men rarely use resistance bands but they are very popular with women, are quite versatile, and effective. Women also might like to add ankle weights if they are buying individual pieces rather than a home gym.
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In summary:
There are so many option from which to choose. I am well aware of that. You have to think about:
1. Your goals - do you want to build muscle, tone and what kind of cardiovascular activities do you like?
2. What is your budget?
3. What kind of space do you have?
4. Will you use what you buy?
5. What kind of experience do you have with equipment?
6. Have you spoken with your doctor before starting an exercise program? If not please do.