Your program can be a life-long endeavor and pleasure. I see mine as the best part of every day. Whether later with weights or machines, or at the beginning without, you get energy and resilience from core and cardio exercises. You will find plenty of great ones using your mat or up on your feet, perhaps with the aid of these props.
A very advanced 70-year body builder explained, “Your muscles don't know how old you are. They will strengthen and grow with training at any age.” This is where you tire your muscles and give them suitable rest to recover with a bit of extra strength. You can probably go farther than you imagine if you proceed slowly and carefully. Doctor and trainer advice first if there are medical issues. That is my main recommendation in this section. However, certain tools suit each exercise, and they are all here.
Any machine will use some of the space in your home gym. If your space permits it, you may find one or more of these things desirable. They only exist because they do some workout task better than can be done without it. However, it must be pointed out that many enthusiasts, with limited space or budget, are completely satisfied with what they are able to do without the help of a machine. That said, no discussion of gym equipment would be complete without describing each and what it can do for you.
One thing everyone cares about in athletic wear is comfort in movement. No one wants to feel restriction as they exercise. If you are doing something that calls for endurance or extra effort, the last thing you want is a nagging discomfort from your clothing. If working out at home, appearance will be of second importance. You may feel differently in a public gym. The makers of athletic clothing rightly assume their clientele are mostly athletes and design more gym apparel for them than they do for us - we older fellas. I try to pay attention to that fact in my recommendations below.