I'm fairly new to the game myself, so hopefully someone will either confirm this or set me straight.
I think the best place for an econ capital is on the planet that has (or will have) the highest population in your empire. IIRC, it boosts (doubles?) the income of the planet that it's built on, and planetary income is based solely on population. It might actually be best, if you have a large, spare planet laying around, to build mostly farms, entertainment centers, and your econ capital there. In my current game, I have a planet that started at 26 PQ and is now somewhere over 30 PQ with just a couple of farms.
Next time I get a planet like that, I'm going to load it up with farms and Virtual Reality modules. "Welcome to Fantasy Planet!"
I haven't had a business capital yet. I tend to put my manufacturing capital and research capital on separate planets and build just factories or labs on the appropriate world. However, next time I get a 700% manufacturing resource planet, I plan to build one factory, both capitals, and a bunch of labs. And a really big military starbase in orbit!!
Love the username - I have to admit that before I bought the game, I was hoping that the Oscillation Overthruster would show up somewhere in the tech tree!