Of course greens fit into Indian cooking! That's what saag paneer is anyway, and spinach and other greens are used a lot, since so many of their folks are vegetarian.
On what to get at the indian store...
spices you ought to pick up:
kalonji/nigella seeds: an extremely tasty addition to indian breads.
methi/fenugreek seeds: great addition to any spice mixture or curry powder.
jeera/cumin: bedrock spice...you need this in quantity.
coriander seed: usually cheap, pick up a bagful.
amchur powder: made from green dried mangos, a good souring agent.
choti elaichi/green cardamom: use with care, very strong.
turmeric: where all the yellow comes from, but also a nice flavor addition.
imli/tamarind: used in many recipes for souring.
black mustard seeds: useful for many recipes, whole or ground.
whole dried red chilies: delicious heat! you can use fresh ones too but I like the red indian dried ones.
saunf/fennel: great for many styles of cooking, not just indian.
garam masala: I know you should make your own, but I like having the commercial stuff on hand.
spices I would consider optional:
anardana/pomegranate seeds: I grind these up to add sourness to aloo samosa filling. Not really necessary though.
kokum: put it this way, I haven't even tried cooking with it yet...but I'll get to it...
kala jeera/black cumin: this is a regional spice and is subtle enough that I think you might not notice its absence...to some extent I don't.
methi/fenugreek leaves: the leaves that I bought adding a funky taste, stick with the seeds at the beginning, but it might be nice to have on hand for recipes.
ajwain/carom: similar to thyme...not ubiquitous, optional.
kali elaichi/black cardamom: I use it a lot but its not often called for.
hing/asafetida: skip this in a big way unless you have a secure place to store it...it reeks, uncooked.
kala namak/black salt: an aromatic pink salt.
gur/jaggery: I have a block of this to sweeten dal slightly but I imagine cheap brown sugar would work perfectly fine.
other things to pick up while you are there:
dal: perhaps chana or toor dal (not the kind stored in oil)
atta or chapati flour (a sort of whole wheat bread flour)
gram/chickpea/besan flour (good for fritters and fried fish)
garlic and ginger...I buy these from my normal market, but whereever you get them, you'll need them, unless you're cooking for Jains, who abstain from garlic for religious reasons.
likewise plain yogurt is another essential ingredient in many cases.