Kasimal has the basics right.
I disagree with the assessment that a little country can't expand and research at the same time, though. It's a bit of a fine balance, but there are some things you can do to expand and research at the same time:
1. Restrict yourself to same-culture provinces. Conquering a province of the same culture will not reduce the number of citizens.
2. Enact laws and national ideas to increase Freedmen to Citizen growth. This is dangerous, though, since you may run low on Freedmen (and, therefore, manpower).
3. You can start by being expansionist, keeping high Freedmen numbers but low Citizen numbers, and then switching to research a little later with high Citizens and low Freedmen. Then you can balance everything out and be able to do both at the same time.
Hope that helps.