Three different-colored Thai curry pastes, how are they different

I think @roux is generally right, curries are like mexican moles, they have lots of spices and are fairly complex. But I do think there are some short-cuts.

The most important components in a curry are sweetness, creaminess, heat, citrus, salt, and depth. I don't know if by simple you also mean you want to use common ingredients, or just 'few' ingredients. This is what I would use if I only had common ingredients:

Coconut milk, cayenne pepper, onion/garlic/ginger, lemon/lime juice, salt/pepper, sugar/honey. I'd also add basil/cilantro/jalapeno for green, tumeric/cumin for yellow, ketchup/tomato paste/chili powder for red.

If you have them, the traditional ingredients you're trying to replicate are lemongrass, lime-leaf, red or green chiles, and fish sauce (or soy sauce).

First, start your Thai coconut curry sauce in a separate pot (i.e. the coconut milk and later the seasonings; no meat , no vegetables, etc.). Make sure to shake the can of coconut milk before opening to ensure it is not separated. Add 1/2 the can to the pot. Bring to boil, reduce temperature and allow the mixture to reduce to almost a paste like texture. This will allow the coconut flavors to intensify, and give you a thicker starting point.

The key is to reduce some of your sauce before cooking everything else; if you attempt to reduce your entire sauce with the vegetables, they will overcook because the process takes too long. Once reduced, add the other 1/2 of the coconut mixture. You end up with a very silky, smooth coconut sauce. Afterwards add your curry paste, fish sauce, sugar, Thai basil etc.