The secret to making amazing Thai curries is to use plenty of aromatics (like onion, ginger and garlic), full-fat coconut milk for richness (you won’t regret it!), and just a little bit of rice vinegar and sugar, which add loads of complexity. Readily available store-bought Thai red curry paste adds characteristic Thai flavor and, bonus, it’s vegetarian, too. You can make your own if you’re so inclined, though.
You should be able to find everything you need for this simple curry at a well-stocked grocery store. Feel free to change up the vegetables, as long as you slice them so they’re all pretty small and about the same size. You could try broccoli, cauliflower, mushrooms, diced butternut or sweet potato (which will probably require a longer cooking time), sliced zucchini and/or yellow squash.