If there’s an Indian/Asian store where you live, they should generally have everything you’d need. The spices are generally divided in to whole spices and ground spices.
For whole spices, commonly used ones are bay leaves, cardamom, cinnamon, cloves, star anise, saffron, mace, and peppers (dried red chillies and black peppercorns).
For ground spices, most common ones are turmeric, chilli powder, coriander powder, cumin powder, asafoetida powder, garam masala and curry powder.
There are also some key seeds and lentils, such as mustard seeds, coriander seeds, cumin seeds, fennel seeds, urad dal
Finally, there are fresh ingredients like curry leaves and coriander leaves, and of course, the usual ones such as ginger/garlic/onions/tomatoes, which you should already have in your pantry/fridge.
With the above in your pantry, you can cook a vast majority of the dishes, at least, as far as spices are concerned.
As for figuring out how they work together, if you follow a few recipes you’ll notice common patterns, so once you’ve got a few dishes under you belt you’d start to recognize which ones you’d need. Easiest way to figure out how they work is to repeat a dish you’ve made and exclude a particular spice, or say doubling the quantity of a particular spice so that it dominates. With so many permutations and combinations possible, you could prepare a dish differently each time and keep things interesting, it’s so much fun playing around with this stuff!