Welfare is the key index in this game. There are TONS of discussions about it if it is worth it or not. Higher welfare means more expenses in general.
I am, and always have been, that it is highly overated. You can easily run a 30country empire with only low to average welfare. Just make sure you put most of your corps in your ceo and accept that you sometimes need to rebuild some things.
You can buy upgrades directly in the war menu where your units are.