Ingredients to Get Started with Indian Cuisine
Indian foods uses a lot of spices. Almost in a level that you will find one new spice in every new recipe.

Still the most common spices AFIK are the follows in the decreasing order of frequency of use


Turmeric powder
Coriander powder
Cumin powder and seeds
Chili powder (You can replace with green chilies if you must)
Garam masala
Dried red chilies
Black peppers


Also asafoetida, fresh coriander leaf, whole cumin seeds, whole mustard seeds. Also, if you can get some ajowan, get it: While not useful in every recipe, it is really great in eg samosas and tikka marinades.

Also, these are very commonly used ingredients


Garlic
Ginger
Onion
Green chili peppers
Tomato
...
Cashew nuts for added thickening (as a paste of boiled cashew nuts) or whole as an ingredient (or both - cashew-thickened real korma with sundry vegetables, dried fruits, and whole cashews added is mind blowing - bring on the saffron too!).


Also always make some yogurt (Unflavored and unsweetened) available

Most common vegetables are


Cauliflower
Cabbage
Potato
Bell peppers (Green)
Red Kidney Beans 


Most common grains are


Rice (Basmati rice is considered as delicacy)
Dal (Many varieties, but you might need mung bean, lentil, toor daal, urid dal )
Whole wheat flour and normal flour


Traditionaly different kind of oils are used but now a days mostly vegitable oil is used. You will also need ghee (Similar to clarified butter) to make some complex and rich dishes.