Economy is the most profitable research, because it increases your gross income directly, without adding any kind of drawbacks.
Welfare increases population, makes your income bigger, but also comes with some drawbacks. More pop is more food loss, more pop is more nw wich means reduced science and more need for units etc.
Early you might want to start out with economy, because most your planets might not benefit from the welfare science etc, towards end of round you want to have them almost even as they are multiplied with eachother when calculating income, so it gives you the best return for you science investment.
When to research:
What you can do if you wonder is a simple calculation:
How much more income will you get if you spend say 10 mill cash in buildings (LQs/TOs)
How much more income will you get if you fund 10 mill cash into eco science?
When popping id say as a rough estimate, get science when you hit around 100% OB
LORD HELP OREGON