Healthcare: Which form of yoga is best, based on health benefits?

Last semester I took world religions and learned a little about yoga. There are a few different types and I’ve read about how the different types do different things. Some are used for weight-loss or stress relief and others are used for strength or flexibility and stuff like that. I want to know which ones do what and how to do the different types. I’m really passionate about yoga and it’s my favorite type of exercise (besides running) that I like. I hate going to the gym, I’d rather run outside and do some yoga after. But I want to know what kind of yoga to do! For example, when I’m feeling stressed, I’d do this type and when I’m trying to break a sweat I’d do this type. Also, what long-term benefits do yoga have? I know some of the short term like improved posture, flexibility and so on but what benefits can it give you in the long term? Like is it good for your circulatory system? Does it help you with long-term memory or anything like that? And which ones do what?