Regular exercise is known to help the mind. For some reason a rating improvement can motivate people far more than longevity, though several UK Grandmasters have recently expressed an interest in exercise and veggies in order to outlive colleague(s)!
Aerobic exercise seems to be to the main type for brain benefits. Rather than join a gym I’ve found that having an exercise bike at home saves time and money. Some people may find things like riding an exercise bike rather boring, in which case they could take up some sport with aerobic benefits. My son Sam and I have been playing a lot of table tennis of late, which is both fun and very healthy.
The incidental effect aerobic exercise has of stress relief can be tackled more directly by breathing exercises, yoga, tai chi and meditation. I’ve been practicing tai chi for around a decade now and it really has helped a lot in terms of relaxation and stress relief.
On the other hand it does not really get the heart beating. So probably the way to go is to practice both an aerobic and a meditative type, for example running plus yoga or table tennis plus tai chi.