I agree that losing weight quickly isn't a good idea for a few reasons: one is that you're more likely to gain it back. Another reason is that the faster you lose, the higher the percentage of weight loss is coming from muscle instead of fat. A slow and steady rate of weight loss (typically 1-2 lbs/wk) is the best way to go.
The best type of exercise (regardless of your medical conditions) is one that you enjoy. That way you're more likely to stick with it. As long as what you're doing is challenging and you like it, that's what is most important.
Hope that helps,