What I'm not clear about is whether "good cholesterol" is actually good for you, or just less bad.

So, does "fish oil (which contains omega-3 fatty acids) increases HDL in a lot of people" - mean, it increases the amount of HDL in you, and that's a good thing; or is it a matter of it increasing the proportion of your cholesterol that is HDL rather than LDL, but ideally you'd want to keep both down?