45 minutes of sustained aerobic exercise at least 3 times a week or every day ideally if you can fit it in. The method of action is probably neurogenesis in the hippocampus which is the brain region responsible for forming new memories but may also play a dominant role in associating information that the brain is already storing with new information aka problem solving.
Anything that will get your heartrate into zone 2 and keep it there for the duration of the exercise. It really depends on what you prefer to do since being consistent with it is the most important thing. If you're unsure, you could always join a gym with a decent selection of equipment and try each of the machines for a week and see which one you feel like sticking with. If you don't want to go to a gym then your options are more limited, pretty much just the ones you listed.
If you don't really do any exercise at all at the moment I'd recommend starting with just walking for 45 minutes, you'll need to do that or some other low intensity exercise for a while to build up to being able to doing 45 minutes of fairly intense cardio. Do a search on YouTube for "how to start running" and you'll find a lot of good plans that you can use and they generalize pretty well to other types of cardio.
Sports should count towards aerobic right? It is hard to find partners and teammates as we age. So individual sports like tennis, squash, etc. Seen plenty of older folks playing those also.
I think forms of martial arts are also fun and sustainable long term. Cycling as a group also good fun.
Cycling and swimming are the only ones that come to mind.