I research improvements in the following order to take care of this problem:
~Xeno Research (Allows you to build Xeno Labs and takes very little time, and clears the way for Stellar Cartography if you don't already have it)
~Stellar Cartography (Allows you to see planets on your minimap, if you don't already, so you know where to send your initial colony ships)
~New Propulsion Techniques (Allows you to get the HyperDrive Plus, though it is more practical to wait until you get the Ion Drive)
~Ion Drive (Allows you to get the Ion Drive and greatly improve your speed)
~Planetary Improvements (This seems to be a given, because it both increases production/research and clears the way for the next series of improvements)
~Impulse Drive (Gives +1 to all of your ships' movement speeds, and allows your colony ships to move at outrageous speeds for ships built this early in the game. You should have no problem grabbing the planets near you after you upgrade your ships)
~Xeno Communications/Universal Translator (This doesn't take very long and allows you to establish communications with neighboring civilizations, who you will probably have encountered by now. You may want to wait on this, because it is doubtful your diplomacy will be great enough to secure a meaningful exchange of technology, and their economy is usually deep in red or will be soon)
~Xeno Economics (Gives me basic economic facilities so I can begin to control my deficit spending)
~Xeno Industrial Theory (By this time, I should have most of my basic factories up and running, so the transition will be smooth)
~All the rest of the Economic Improvements (They take the least amount of time to research and build, and the Stock Market is outrageous! It gives a bonus to your economy, influence, and morale

If you can get these up, then your economy should florish, at least as soon as you can get enough of a taxable population to get out of deficit spending)
After this, your economy should begin to stabilize and your Factories should be completed, so you can start the next round of upgrades or whatever else you want. You usually have sufficient research capabilities to complete Research Academies in a few weeks.