Empire Priority - what resources your empire wants, based on what it has and what it needs
Galaxy Priority - what resources everyone in the galaxy, taken as a whole, want, based on what everyone has and what everyone needs.
Personally, I almost always look at Galaxy Priority, because Empire Priority has an unfortunate tendency to filter out resource deposits that the game thinks your empire doesn't need to mine.
Also when I am looking research do I add up all 3 bottom totals to see if it is equal to total empire research potential or does each area need to be that high?
If you want to max out your research, then take the capacities in each area, add them up, and compare them to your empire potential. If the total capacity is at least equal to the empire potential, then you're maxed out on research for the bonuses you have available and the current empire research potential.
P.S. Best way to make money early game?
Private sector construction is probably the biggest short-term money-earner. They'll build a bunch of stuff when you complete the space port, and they'll build more stuff each time you colonize something.
Longer term, probably taxing the homeworld, though there's a tradeoff between population growth and tax rate. Resort bases might also be worth a look, if you can get a scenery bonus somewhere close by.