I found this on how exercise improves our brain function. It may answer your questions. www.fi.edu/learn/brain/exercise.html#physi
A nutritious, balanced diet is the most important thing to weight loss. Strength training is the second most important part of the equation, and cardio comes in last. I never focused much on strength training and did almost all cardio and yeah, I lost 50 pounds, but I lost a lot of muscle in the process. If you want to lose weight, I suggest you focus more on strength training than cardio. And of course eat a healthy, balanced diet. SparkPeople has beginner videos for strength training. You can also do body weight exercises, which I love. As far as equipment goes, dumbbells aren't that expensive, but the problem I'm facing now is that I have to go out and buy heavier dumbbells. Obviously the heavier they are, the more they cost. If you can, take advantage of the equipment your mom's gym has since strength training is a huge part of weight loss. Start small though. Don't push yourself too hard in the beginning because you'll probably get tired of it.