There are 2 ways of practicing martial arts for health.
One way is to practice alone, at home, by doing some solo forms (a.k.a. kata) taken from the large existing number of Okinawan or Chinese origin, with or without weapons, and/or by hitting dummies or punching bags.
This way has the advantage of minimal cost, down to zero, depending on whether you buy some training equipment and weapons or not, and you can practice without following a schedule, whenever you have time or you are in the mood.
Practicing solo is easy if you have some prior experience of doing proper training sessions in some martial art. Even without experience, if the purpose is only practicing for health and not becoming skilled in real fighting, some instructional videos can be good enough for learning how to train.
The second way is to practice with a sparring partner. Sometimes this might be possible to do with a friend, if you happen to have an appropriate space, but this is quite unlikely, so you normally have to go regularly to some martial arts training hall or club.
In this case the choice of the martial art may be determined less by some intrinsic qualities, but more by what martial art training place happens to exist close enough to your home, to avoid wasting time with transportation.
Moreover, especially when practicing for health purposes, it may be less important which is the origin of the martial art, but much more important is how competent is the instructor that happens to teach at the club that you find near you.
Unfortunately, for a beginner it is difficult to distinguish competent instructors from incompetent instructors, but after some experience the differences will become evident.
Which martial art is more appropriate depends also on the age. For someone older, a training that puts less emphasis on striking/kicking, but more on throwing and breaking falls, e.g. aikido/judo/jujutsu, is more appropriate. Also training with weapons can be appropriate for older people, as in that case the weapons are not used against humans, unless they wear protective gear.
When practicing any kind of sport, it is necessary to do it in such a way as to avoid accidents.
While it is possible to train in a careless way and suffer consequences, the straining of the wrists and of other articulations in aikido is actually very useful for avoiding the loss of articular mobility that happens to most old people, unless they do regularly other kinds of mobility exercises.
For someone who types a lot, regular mobility exercises for wrists and fingers are very important for avoiding the injuries caused by typing and by using a mouse, which are much more frequent than the aikido injuries.
As a personal anecdote, I have practiced for some time aikido without any kind of injuries, but later, when failing to do regular exercises, I have developed some tendon problems in my right middle finger from the scrolling wheel of the mouse (which I have healed by switching from using a mouse to the use of a stylus on a Wacom tablet in mouse mode; now I wonder why I have used mice/trackballs/touchpads/trackpoints for so many years, because a stylus is much more comfortable).
Not OP, but I’ve taken up training Muay Thai and it’s a lot of fun. It can look pretty intimidating from the outside, but everyone I’ve met at the gyms here in Brooklyn have been super welcoming and kind.
I also have had a long standing, 5x per week yoga practice which is a great way to strengthen and open the body. I’d look for a yoga school that mentions ashtanga if you’re looking for something more intensive, it’s a challenging practice.
Pretty much everyone I’ve ever met who actually knew how to fight well was very friendly and kind. Traveling and showing up at random MMA or BJJ schools is almost always a fantastic experience.
Subjecting the ego to much needed reality checks makes for some nice folks.
Seconded. I worked with a professional MMA team while they appeared on The Ultimate Fighter and met a lot of fighters who came to their gym to train, even spent some time living in a communal house with some of them. All but one of them would be in the running for the “nicest person I ever met” award.