Rich economy = better education = better overall living conditions = more budget for infrastructure = more budget for military power
Once a country gets their economy going then everything just follows suit. When they have the money they can pretty much do anything to be able to improve on their country whether that is to strengthen their defense or just make sure their citizens are being treated well.
If you pay attention with the underdeveloped countries, you will know if those countries aren't poor, they actually have a lot natural resources. While the developed countries, not all of them have natural resources as big as underdeveloped countries, so why it can be like that?
The answer isn't about how rich or poor the country, but how big the corruption rate on that country? it's useless to have a lot natural resources and human resources if the country is full of corruption.