I agree wholeheartedly with you about being respectful by being educated. Especially when dealing with other cultures' religious elements. That's a sensitive subject in itself mainly because religion is often a deeply personal thing. Research, experience, interplay with those active in the religion are crucial when it comes to trying your own hand at representing them. While it's almost impossible to come to a similar, full understanding as a person who's lived their life in a specific religion, it's definitely not outta the cards to learn as much as you can.
Dedicating a lot of time and energy to the subtleties of a particular religion is necessary because it can be extremely easy for you to overlook something and even easier for a person in-the-know to spot your misstep! Even if you have good intentions, you know all about blasphemy and how damning that can be (also raised Catholic, went to Catholic school a couple years here!).
So yes! I think, especially if you're interested in Eastern mythology, definitely start with reading some academic articles. I took several Asian philosophy and history courses while in uni (also fascinated with Eastern mythology and philosophy!), but I barely scratched the surface on things.
Concerning Hindu goddesses, personally, I'd look up on the symbolism and myth origins in tandem with historic icons and pieces of texts they're connected to. Your accumulated research should work like a spider, spinning a web out from the key figures themselves. It'll be really fun, though, the history of ancient myths are always amazing things to learn about. You'll probably be picking up on new ideas as you go!